@Article{AbCaGeLe04,
author = "S. A. Abramov and J. J. Carette and K. O. Geddes and H. Q. Le",
title = "Telescoping in the Context of Symbolic Summation in {M}aple",
journal = "Journal of Symbolic Computation",
year = 2004,
volume = 38,
number = 4,
pages = {1303--1326},
month = Oct
}
@InProceedings{AbLe04,
author = {S. A. Abramov and H. Q. Le},
title = "{Utilizing relationships among linear systems generated
by {Z}eilberger's algorithm}",
booktitle = {Formal Power Series and Algebraic Combinatorics},
year = 2004,
pages = {29--38},
note = {Proceedings of FPSAC'04, Vancouver, June 2004}
}
@Article{AbLe05,
author = "S. A. Abramov and H. Q. Le",
title = "{On the order of the recurrence produced by the method of creative telescoping}",
journal = "Discrete Mathematics",
year =2005,
volume = 298,
number = {1--3},
month = aug,
pages = {2--17}
}
@InProceedings{AdJaRo00,
author = {C\'edric Adjih and Philippe Jacquet and Philippe Robert},
title = {Differentiated admission control in large networks},
booktitle = {INFOCOM 2000},
pages = {1455--1461},
year = 2000,
publisher = {{IEEE}},
address = {Tel Aviv}
}
@inproceedings{AmBeGiHuPe06,
author={O. Amini and J.-C. Bermond and F. Giroire and F. Huc and S. P{\'e}rennes},
title={Design of Minimal Fault Tolerant Networks: Asymptotic Bounds},
booktitle={Huiti\`emes Rencontres Francophones sur les Aspects Algorithmiques des T\'el\'ecommunications (AlgoTel'06)},
address={Tr\'egastel, France},
month=may,
year=2006,
pages={37--40}
}
@article{AtChDu01,
AUTHOR = {Atallah, M. J. and Chyzak, F. and Dumas, P.},
TITLE = {A randomized algorithm for approximate string matching},
JOURNAL = {Algorithmica},
VOLUME = {29},
YEAR = {2001},
NUMBER = {3},
PAGES = {468--486},
Web-comment = {Preliminary version (INRIA Research Report #3194).},
Abstract = {We give a randomized algorithm in deterministic time~$O(N\log M)$ for
estimating the score vector of matches between a text string of
length~$N$ and a pattern string of length~$M$, i.e., the vector
obtained when the pattern is slid along the text, and the number of
matches is counted for each position. A direct application is
approximate string matching. The randomized algorithm bases on
convolution to find an estimator of the scores; the variance of the
estimator is particularly small for scores that are close to~$M$,
i.e., for approximate occurrences of the pattern in the text. No
assumption is made about the probabilistic characteristics of the
input, or about the size of the alphabet. The solution extends to
string matching with classes, class complements, ``never match'' and
``always match'' symbols, to the weighted case and to higher
dimensions.}
}
@Article{AtMo93b,
author = "A. O. L. Atkin and F. Morain",
title = "Elliptic Curves and Primality Proving",
journal = "Mathematics of Computation",
year = 1993,
volume = 61,
number = 203,
month = jul,
url= {http://www.inria.fr/rrrt/rr-1256.html}
}
@Article{AtMo93,
author = "A. O. L. Atkin and F. Morain",
title = "Finding suitable curves for the Elliptic Curve factoring
method",
journal = "Mathematics of Computation",
year = 1993,
volume = 60,
number = 201,
month = jan,
url = {http://www.inria.fr/rrrt/rr-1547.html}
}
@Article{BaBoDeFlGaGo01,
author = {Cyril Banderier and Mireille Bousquet-M{\'e}lou
and Alain Denise and Philippe Flajolet and
Dani{\`e}le Gardy and Dominique Gouyou-Beauchamps},
title = {Generating Functions for Generating Trees},
year = 2000,
journal = "Discrete Mathematics",
note={An earlier version "On Generating Functions of Generating
Trees" was in the proceedings of FPSAC'99 (pp. 40-52)and as INRIA
Report 3661},
url = {http://www.inria.fr/rrrt/rr-3661.html}
}
@Article{BaBoDeFlGaGo02,
author = "Cyril Banderier and Mireille Bousquet-M\'elou and
Alain Denise and Philippe Flajolet and Dani\`ele Gardy and
Dominique Gouyou-Beauchamps",
title = "Generating Functions of Generating Trees",
year = 2002,
month = mar,
journal = "Discrete Mathematics",
volume = 246,
number = "1-3",
pages = "29--55"
}
@InProceedings{BaChLR03,
author = {Barkatou, Moulay and Chyzak, Fr{\'e}d{\'e}ric and Loday-Richaud, Mich{\`e}le},
title = {Remarques algorithmiques li{\'e}es au rang d'un op{\'e}rateur diff{\'e}rentiel lin{\'e}aire},
booktitle = {From Combinatorics to Dynamical Systems (Journ{\'e}es de Calcul Formel, Strasbourg, March 22-23, 2002)},
year = 2003,
pages = {87--129},
editor = {Fauvet, F. and Mitschi, C.},
volume = 3,
series = {IRMA Lectures in Mathematics and Theoretical Physics},
publisher = {de Gruyter},
Note = {In French. ISBN 3-11-017875-3},
Web-comment = {Preliminary version.},
Abstract = {(French) Dans cet article nous d\'ecrivons et comparons
diff\'erentes m\'ethodes algorithmiques pour r\'esoudre le
probl\`eme suivant : \'etant donn\'ee une s\'erie $\hat
f(x)=\sum_{m\geq 0}u_mx^m$ solution d'une \'equation
diff\'erentielle li\-n\'e\-aire ordinaire et un
nombre entier $r>0$, construire une
\'equation diff\'erentielle v\'erifi\'ee par les sous-s\'eries
$\hat f^j(x)=\sum_{m\geq 0}u_{j+mr}x^{j+mr}$ de ses termes de
$r$ en $r$. Cette question appara\^\i t
naturellement lors de l'implantation en calcul formel des
solutions formelles et de leurs (multi-)sommes. Les m\'ethodes
propos\'ees sont implant\'ees en {\sc Maple} et nous
donnons l'adresse des programmes correspondants.\\ En
appendice nous indiquons une d\'emarche constructive
r\'ealiste pour le calcul effectif des invariants formels d'une
\'equation ou d'un syst\`eme.
(English) This paper aims at
introducing and comparing various methods for solving the
following problem which arises naturally in computer algebra
for differential equations: given a series
$\hat f(x)=\sum_{m\geq 0}u_mx^m$ solution of an ordinary linear differential
equation and given an integer $r\geq 2$ find a differential
equation satisfied by the sub-series
$\hat f^j(x)=\sum_{m\geq 0}u_{j+mr}x^{j+mr}$.
These methods have been implemented in {\sc Maple}.
References are given to the corresponding programs.
Possible realistic
algorithms to effectively calculate the formal invariants of
an ordinary linear differential system of order one and
arbitrary rank are sketched in an Appendix.}
}
@InProceedings{BaDo00,
author = {Cyril Banderier and Robert P. Dobrow},
title = {A Generalized Cover Time for Random Walks on Graphs},
year = 2000,
month=jun,
booktitle = {FPSAC'00},
publisher = {Springer},
ISBN = {3-540-67247-8},
pages="113--124",
url = {http://algo.inria.fr/banderier/Papers/Dobrow/walksgraphs.ps}
}
@Article{BaFl02,
title = "Basic Analytic Combinatorics of Directed Lattice Paths",
author = "Cyril Banderier and Philippe Flajolet",
journal = "Theoretical Computer Science",
year = 2002,
volume = "281",
number = "1-2",
pages = " 37--80"
}
@article {BaFl10,
AUTHOR = {Bacher, Roland and Flajolet, Philippe},
TITLE = {Pseudo-factorials, elliptic functions, and continued
fractions},
JOURNAL = {Ramanujan J.},
FJOURNAL = {Ramanujan Journal. An International Journal Devoted to the
Areas of Mathematics Influenced by Ramanujan},
VOLUME = {21},
YEAR = {2010},
NUMBER = {1},
PAGES = {71--97},
ISSN = {1382-4090},
DOI = {10.1007/s11139-009-9186-9},
URL = {http://dx.doi.org/10.1007/s11139-009-9186-9},
}
@InProceedings{BaFlShSo00,
author = {Cyril Banderier and Philippe Flajolet and
Gilles Schaeffer and Mich{\`e}le Soria},
title = {Planar Maps and {A}iry Phenomena},
year = 2000,
month = jan,
booktitle = {ICALP'00},
publisher = {Springer-Verlag},
ISSN="0302-9743",
series = "Lecture Notes in Computer Science",
volume= "1853",
pages="388--402",
url = {http://algo.inria.fr/banderier/Papers/Airy/coal.ps}
}
@Article{BaFlShSo01,
author = {Cyril Banderier and Philippe Flajolet and
Gilles Schaeffer and Mich{\`e}le Soria},
title = {Random Maps, Coalescing Saddles, Singularity Analysis, and {A}iry Phenomena},
journal = "Random Structures \& Algorithms",
volume = 19,
number = "3/4",
pages = "194--246",
year = 2001,
url = {http://algo.inria.fr/flajolet/Publications/rsa0903.ps.gz}
}
@PhDThesis{Banderier01,
author = "Cyril Banderier",
title = "Combinatoire analytique des chemins et des cartes",
year = 2001,
month = jun,
type = {Th{\`e}se de Doctorat},
school = "Universit\'e Paris~VI",
url = {http://algo.inria.fr/banderier/Papers/}
}
@techreport{BardetFaugereSalvySpaenlehauer2011,
Arxiv = {abs/1112.6263},
Author = {Bardet, Magali and Faug{\`e}re, Jean-Charles and Salvy, Bruno and Spaenlehauer, Pierre-Jean},
Date-Added = {2012-01-02 06:14:07 +0000},
Date-Modified = {2012-01-02 06:15:26 +0000},
Eprint = {1112.6263},
Institution = {arXiv},
Month = dec,
Title = {On the Complexity of Solving Quadratic Boolean Systems},
Url = {http://arxiv.org/abs/1112.6263},
Year = {2011},
Bdsk-Url-1 = {http://arxiv.org/abs/1112.6263},
Abstract = {A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over ${F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in $4\log_2 n\,2^n$ operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step.
Under precise algebraic assumptions, we show that the deterministic variant of our algorithm has complexity bounded by $O(2^{0.841n})$ when $m=n$, while a probabilistic variant of the Las Vegas type has expected complexity $O(2^{0.792n})$.
Experiments on random systems show that the algebraic assumptions are satisfied with probability very close to~1.
We also give a rough estimate for the actual threshold between our method and exhaustive search, which is as low as~200, and thus very relevant for cryptographic applications.},
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@article{BBGHJMZ09,
author = {A. Bostan and S. Boukraa and A. J. Guttmann and S. Hassani and I. Jensen and J.-M. Maillard and N. Zenine},
title = {High order {F}uchsian equations for the square lattice {I}sing model: $\tilde{\chi}^{(5)}$},
journal = {J. Phys. A: Math. Theor.},
number = {27},
year = {2009},
volume = {42},
pages = {32pp},
doi = {10.1088/1751-8113/42/27/275209},
abstract = {We consider the Fuchsian linear differential equation obtained (modulo a prime) for $\tilde{\chi}^{(5)}$, the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of $\tilde{\chi}^{(1)}$ and $\tilde{\chi}^{(3)}$ can be removed from $\tilde{\chi}^{(5)}$ and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth order linear differential operator occurs as the left-most factor of the ``depleted" differential operator and it is shown to be equivalent to the symmetric fourth power of $L_E$, the linear differential operator corresponding to the elliptic integral $E$. This result generalizes what we have found for the lower order terms $\tilde{\chi}^{(3)}$ and $\tilde{\chi}^{(4)}$. We conjecture that a linear differential operator equivalent to a symmetric $(n-1)$-th power of $L_E$ occurs as a left-most factor in the minimal order linear differential operators for all $\tilde{\chi}^{(n)}$'s.},
}@article{BBHHMWZ10,
author = {Bostan, A. and Boukraa, S. and Hassani, S. and van Hoeij,
M. and Maillard, J.-M. and Weil, J.-A. and Zenine, N.},
title = {The {I}sing model: from elliptic curves to modular forms
and {C}alabi-{Y}au equations},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {44},
number = {4},
year = {2011},
pages = {44pp},
doi = {10.1088/1751-8113/44/4/045204},
arxiv = {abs/1007.0535},
abstract = {We show that almost all the linear differential operators
factors obtained in the analysis of the $\, n$-particle contributions $\,
{\tilde \chi}^{(n)}$'s of the susceptibility of the Ising model for $\, n
\le 6$, are linear differential operators ``{\em associated with elliptic
curves}''. Beyond the simplest differential operators factors which are
homomorphic to symmetric powers of the second order operator associated
with the complete elliptic integral $\, E$, the second and third order
differential operators $\, Z_2$, $\, F_2$, $\, F_3$, $\, {\tilde L}_3$ can
actually be interpreted as {\em modular forms} of the elliptic curve of
the Ising model. A last order-four globally nilpotent linear differential
operator is not reducible to this elliptic curve, modular forms scheme.
This operator is shown to actually correspond to a natural generalization
of this elliptic curve, modular forms scheme, with the emergence of a
Calabi-Yau equation, corresponding to a selected $_4F_3$ hypergeometric
function. This hypergeometric function can also be seen as a Hadamard
product of the complete elliptic integral $\, K$, with a remarkably simple
algebraic pull-back (square root extension), the corresponding Calabi-Yau
fourth-order differential operator having a symplectic differential Galois
group $\, SP(4, \, \mathbb{C})$. The mirror maps and higher order
Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice
physical and mathematical ingredients we had with elliptic curves and
modular forms, in particular an exact (isogenies) representation of the
generators of the renormalization group, extending the modular group
$SL(2, \, \mathbb{Z})$ to a $GL(2, \, \mathbb{Z})$ symmetry group.},
}@article{BBHMWZ09,
author = {A. Bostan and S. Boukraa and S. Hassani and J. -M. Maillard and J. -A. Weil and N. Zenine},
title = {Globally nilpotent differential operators and the square {I}sing model},
journal = {J. Phys. A: Math. Theor.},
number = {12},
year = {2009},
volume = {42},
doi = {10.1088/1751-8113/42/12/125206},
pages = {50pp},
abstract = {We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.},
}
@article{BBHMWZA10,
author = {Bostan, A. and Boukraa, S. and Hassani, S. and Maillard,
J.-M. and Weil, J.-A. and Zenine, N. and Abarenkova, N.},
title = {Renormalization, isogenies and rational symmetries of
differential equations},
journal = {Advances in Mathematical Physics},
volume = {2010},
pages = {44pp},
year = {2010},
doi = {10.1155/2010/941560},
arxiv = {abs/0911.5466},
abstract = {We give an example of infinite order rational
transformation that leaves a linear differential equation covariant. This
example can be seen as a non-trivial but still simple illustration of an
exact representation of the renormalization group.},
}@article {BeFlGu10,
AUTHOR = {Beaton, Nicholas R. and Flajolet, Philippe and Guttmann,
Anthony J.},
TITLE = {The unusual asymptotics of three-sided prudent polygons},
JOURNAL = {J. Phys. A},
FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
VOLUME = {43},
YEAR = {2010},
NUMBER = {34},
PAGES = {342001, 10},
DOI = {10.1088/1751-8113/43/34/342001},
URL = {http://dx.doi.org/10.1088/1751-8113/43/34/342001},
}
@MASTERSTHESIS{Benoit09,
Author = {Benoit, Alexandre},
title = {D{\'e}veloppements de fonctions {D}-finies sur des polyn{\^o}mes de {T}chebychev},
school = {Universit{\'e} Paris VI-MPRI},
Type = {Rapport de stage},
url = {http://algo.inria.fr/papers/pdf/Benoit2008.pdf},
Year = {2008}
}
@inproceedings{BenoitChyzakDarrasseGerholdMezzarobbaSalvy2010,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Benoit, Alexandre and Chyzak, Fr{\'e}d{\'e}ric and Darrasse, Alexis and Gerhold, Stefan and Mezzarobba, Marc and Salvy, Bruno},
Booktitle = {The Third International Congress on Mathematical Software (ICMS 2010)},
Date-Added = {2010-08-16 07:19:29 +0200},
Date-Modified = {2010-09-22 15:15:38 +0200},
Doi = {10.1007/978-3-642-15582-6_7},
Editor = {Fukuda, Komei and van der Hoeven, Joris and Joswig, Michael and Takayama, Nobuki},
Pages = {35--41},
Series = {Lecture Notes in Computer Science},
Title = {The Dynamic Dictionary of Mathematical Functions ({DDMF})},
Volume = {6327},
Year = {2010},
Abstract = {We describe the main features of the Dynamic Dictionary of Mathematical Functions (version 1.5). It is a website consisting of interactive tables of mathematical formulas on elementary and special functions. The formulas are automatically generated by computer algebra routines. The user can ask for more terms of the expansions, more digits of the numerical values, or proofs of some of the formulas.
}}
@inproceedings{BenoitSalvy2009,
Arxiv = {abs/0906.2888},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Benoit, Alexandre and Salvy, Bruno},
Booktitle = {ISSAC '09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation},
Date-Added = {2009-06-16 21:20:53 +0200},
Date-Modified = {2009-08-03 14:30:50 +0200},
Doi = {10.1145/1576702.1576709},
Editor = {May, John},
Pages = {23--30},
Title = {Chebyshev Expansions for Solutions of Linear Differential Equations},
Year = {2009},
Abstract = {A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.
}
}
@Misc{Besson06,
author = "Besson, Bruno",
title = "Matrices poids-position : principes et algorithmes",
year = 2006,
note = "M\'emoire de Master 2, Universit\'e Paris XI",
url = {http://algo.inria.fr/papers/pdf/Besson06.pdf},
}
@article{BlasiakFlajolet2011,
Author = {Blasiak, Pawel and Flajolet, Philippe},
Date-Added = {2011-06-13 12:51:29 +0200},
Date-Modified = {2011-12-07 06:48:03 +0000},
Journal = {S{\'e}minaire Lotharingien de Combinatoire},
Number = {B65c},
Pages = {1--78},
Title = {Combinatorial models of creation-annihilation},
Url = {http://www.emis.de/journals/SLC/wpapers/s65blafla.pdf},
Volume = {65},
Year = {2011},
Abstract = {Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial structures and the reduction to normal form of operator polynomials in such an algebra. The connection is achieved through suitable labelled graphs, or "diagrams", that are composed of elementary "gates". In this way, many normal form evaluations can be systematically obtained, thanks to models that involve set partitions, permutations, increasing trees, as well as weighted lattice paths. Extensions to q-analogues, multivariate frameworks, and urn models are also briefly discussed.
},
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@inproceedings{BoChChLi10,
author = {Bostan, Alin and Chen, Shaoshi and Chyzak, Fr\'{e}d\'{e}ric and Li, Ziming},
title = {Complexity of creative telescoping for bivariate rational functions},
booktitle = {ISSAC'10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation},
year = {2010},
pages = {203--210},
location = {Munich, Germany},
doi = {http://doi.acm.org/10.1145/1837934.1837975},
publisher = {ACM},
address = {New York, NY, USA},
abstract = {The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain tight degree bounds on the various expressions involved in the method. To make the problem more tractable, we restrict to \emph{bivariate rational\/} functions. By considering this constrained class of inputs, we are able to blend the general method of creative telescoping with the well-known Hermite reduction. We then use our new method to compute diagonals of rational power series arising from combinatorics.},
}
%% Created for Bruno Salvy at 2008-04-24 11:35:57 +0200
%% Saved with string encoding Unicode (UTF-8)
@inproceedings{BoChClSa06,
Arxiv = {abs/cs/0605068},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Cluzeau, Thomas and Salvy, Bruno},
Booktitle = {ISSAC'06},
Date-Added = {2006-03-23 22:02:47 +0100},
Date-Modified = {2008-04-24 11:35:52 +0200},
Doi = {10.1145/1145768.1145781},
Editor = {Dumas, Jean-Guillaume},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoChClSa06.pdf},
Pages = {31--38},
Publisher = {ACM Press},
Title = {Low Complexity Algorithms for Linear Recurrences},
Year = {2006},
Abstract = {We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are hypergeometric over the rational numbers.
The algorithms for these tasks all involve as an intermediate quantity an integer~$N$ (dispersion or root of an indicial polynomial) that is potentially exponential in the bit size of their input. Previous algorithms have a bit complexity that is at least quadratic in~$N$. We revisit them and propose variants that exploit the structure of solutions and avoid expanding polynomials of degree~$N$. We give two algorithms: a probabilistic one that detects the existence or absence of nonzero polynomial and rational solutions in~$O(\sqrt{N}\log^{2}N)$ bit operations; a deterministic one that computes a compact representation of the solution in~$O(N\log^{3}N)$ bit operations. Similar speed-ups are obtained in indefinite and definite hypergeometric summation. We describe the results of an implementation.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1145768.1145781}}
@article{BoChHoSc10,
author = {A. Bostan and M.F.I. Chowdhury and J. van der Hoeven and
{\'E}. Schost},
title = {Homotopy methods for multiplication modulo triangular
sets},
journal = {Journal of Symbolic Computation},
year = {2011},
volume = {46},
number = {12},
pages = {1378--1402},
abstract = {We study the cost of multiplication modulo triangular
families of polynomials. Following previous work by Li, Moreno Maza and
Schost, we propose an algorithm that relies on homotopy and fast
evaluation-interpolation techniques. We obtain a quasi-linear time complexity
for substantial families of examples, for which no such result was known
before. Applications are given to notably addition of algebraic numbers in
small characteristic.},
}
@inproceedings{BostanChyzakLecerfSalvySchost2007,
Arxiv = {cs.SC/0703121},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Chyzak, Fr\'ed\'eric and Lecerf, Gr\'egoire and Salvy, Bruno and Schost, \'Eric},
Booktitle = {ISSAC'07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation},
Date-Added = {2007-02-12 14:06:40 +0100},
Date-Modified = {2009-10-05 08:46:29 +0200},
Doi = {10.1145/1277548.1277553},
Editor = {Brown, C. W.},
Pages = {25--32},
Publisher = {ACM Press},
Title = {Differential equations for algebraic functions},
Year = {2007},
Abstract = {It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove the existence of recurrences of order and degree close to optimal. We study the complexity of computing these differential equations and recurrences. We deduce a fast algorithm for the expansion of algebraic series.
}
}
@misc{BoChLiSa11,
author = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Li, Ziming and Salvy, Bruno},
title = {Fast computation of common left multiples of linear ordinary differential operators},
journal = {ACM Commun. Comput. Algebra},
issue_date = {March/June 2011},
volume = {45},
issue = {1/2},
month = {July},
year = {2011},
issn = {1932-2240},
pages = {111--112},
numpages = {2},
url = {http://doi.acm.org/10.1145/2016567.2016581},
doi = {http://doi.acm.org/10.1145/2016567.2016581},
acmid = {2016581},
publisher = {ACM},
howpublished = {Poster at ISSAC 2011},
address = {New York, NY, USA},
}
@inproceedings{BoChLR08,
Arxiv = {abs/0804.2181},
Author = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Le Roux, Nicolas},
Booktitle = {ISSAC'08 (July 20--23, 2008, Hagenberg, Austria)},
Date-Modified = {2008-04-23 09:37:49 +0200},
Note = {Conference proceedings},
Pages = {23--30},
Publisher = {ACM},
Title = {Products of Ordinary Differential Operators by Evaluation and Interpolation},
Year = {2008},
abstract = {It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products.
We give a new algorithm by evaluation and interpolation that is faster than the previously-known one by a constant factor, and
prove that in characteristic zero, multiplication of differential operators and of matrices are computationally equivalent problems.
In positive characteristic, we show that differential operators can be multiplied in nearly optimal time.
This equivalence fails in positive characteristic and we give an algorithm that multiplies differential operators in nearly linear time when the characteristic is small.
Theoretical results are validated by intensive experiments.}
}
%% Created for Bruno Salvy at 2008-04-24 11:36:43 +0200
%% Saved with string encoding Unicode (UTF-8)
@inproceedings{BoChOlSaScSe07,
Arxiv = {abs/cs/0604101},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Ollivier, Fran{\c c}ois and Salvy, Bruno and Schost, {\'E}ric and Sedoglavic, Alexandre},
Booktitle = {SODA'07},
Date-Added = {2006-04-26 17:08:09 +0200},
Date-Modified = {2008-04-24 11:36:43 +0200},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoChOlSaScSe07.pdf},
Month = jan,
Note = {Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, New Orleans, Louisiana},
Pages = {1012--1021},
Publisher = {Society for Industrial and Applied Mathematics},
Title = {Fast computation of power series solutions of systems of differential equations},
Year = {2007},
Abstract = {We propose new algorithms for the computation of the first~$N$ terms
of a vector (resp. a basis) of power series solutions of a linear
system of differential equations at an ordinary point, using a
number of arithmetic operations which is quasi-linear with respect
to~$N$. Similar results are also given in the non-linear case. This extends
previous results obtained by Brent and
Kung for scalar differential equations of order one and two.},
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@article{BoClReRoMa07,
Author = {Boeva, Valentina and Cl\'ement, Julien and R\'egnier, Mireille and Roytberg, Mikhail and Makeev, Vsevolod},
Date-Added = {2007-12-10 17:55:59 +0100},
Date-Modified = {2007-12-10 17:59:01 +0100},
Journal = {Algorithms for molecular biology},
Number = {13},
Pages = {25 pages},
Title = {Exact p-value calculation for heterotypic clusters of regulatory motifs and its application in computational annotation of cis-regulatory modules},
Volume = {2},
Year = {2007},
Url = {http://www.almob.org/content/2/1/13}
}
@string{LNCS = "Lecture Notes in Computer Science"}
@Inproceedings{BoClReVa05,
author = "V. Boeva and J. Cl{\'e}ment and M. R{\'e}gnier and M. Vandenbogaert",
title = "Assessing the significance of {S}ets of {W}ords",
year = "2005",
booktitle = "Combinatorial Pattern Matching 05",
series = LNCS,
volume = 3537,
publisher = "Springer Verlag",
pages = "358--370",
note = "In Proceedings CPM'05, Jeju Island, Korea",
url = {http://algo.inria.fr/regnier/publis/BoClReVa05.ps}
}
@article{BoCo11,
author = {Bostan, Alin and Combot, Thierry},
title = {A binomial-like matrix equation},
journal = {American Mathematical Monthly},
year = {To appear},
abstract = {We show that a pair of matrices satisfying a certain algebraic identity, reminiscent of the binomial theorem, must have the same characteristic polynomial. This is a generalization of Problem 4 (11th grade) from the Romanian National Mathematical Olympiad 2011.}
}
@article{BoDu10,
author = {Bostan, Alin and Dumas, Philippe},
title = {{W}ronskians and linear independence},
journal = {American Mathematical Monthly},
volume = {117},
number = {8},
pages = {722--727},
year = {2010},
abstract = {We give a new and simple proof of the fact that a finite
family of analytic functions has a zero Wronskian only if it is linearly
dependent.},
}@article {BoFl09,
AUTHOR = {B{\'o}na, Mikl{\'o}s and Flajolet, Philippe},
TITLE = {Isomorphism and symmetries in random phylogenetic trees},
JOURNAL = {J. Appl. Probab.},
FJOURNAL = {Journal of Applied Probability},
VOLUME = {46},
YEAR = {2009},
NUMBER = {4},
PAGES = {1005--1019},
DOI = {10.1239/jap/1261670685},
URL = {http://dx.doi.org/10.1239/jap/1261670685},
}@article{BoGaSc07,
author = {A. Bostan and P. Gaudry and \'E. Schost},
title = {Linear recurrences with polynomial coefficients and
application to integer factorization and {C}artier-{M}anin operator},
journal = {SIAM Journal on Computing},
number = {6},
pages = {1777--1806},
volume = {36},
year = {2007},
abstract = {We study the complexity of computing one or several terms
(not necessarily consecutive) in a recurrence with polynomial coefficients.
As applications, we improve the best currently known upper bounds for
factoring integers deterministically, and for computing the Cartier-Manin
operator of hyperelliptic curves.},
}@inproceedings{BoJeSc07,
author = {Bostan, Alin and Jeannerod, Claude-Pierre and Schost, \'Eric},
title = {Solving {T}oeplitz- and {V}andermonde-like Linear Systems with
Large Displacement Rank},
booktitle = {ISSAC'07: Proceedings of the 2007 international symposium
on Symbolic and algebraic computation},
year = {2007},
editor = {Brown, C. W.},
publisher = {ACM Press},
pages = {33--40},
doi = {10.1145/1277548.1277554},
abstract = {Linear systems with structures such as Toeplitz-, Vander\-monde- or
Cauchy-likeness can be solved in $\tilde O (\alpha^2 n)$ operations,
where $n$ is the matrix size, $\alpha$ is its displacement rank, and
$\tilde O (\,)$ denotes the omission of logarithmic factors. We show that
for Toeplitz-like and Vandermonde-like matrices, this cost can be
reduced to $\tilde O (\alpha^{\omega-1} n)$, where $\omega$ is a
feasible exponent for matrix multiplication over the base field.
The best known estimate for $\omega$ is $\omega < 2.38$, resulting in
costs of order $\tilde O (\alpha^{1.38} n)$. We also present consequences
for Hermite-Pad\'e approximation and bivariate interpolation.},
}
@article{BoJeSc08,
author = {Bostan, Alin and Jeannerod, Claude-Pierre and Schost, \'Eric},
title = {Solving structured linear systems with large displacement rank},
journal = {Theoretical Computer Science},
volume = {407},
number = {1-3},
year = {2008},
pages = {155--181},
doi = {http://dx.doi.org/10.1016/j.tcs.2008.05.014},
publisher = {Elsevier Science Publishers Ltd.},
address = {Essex, UK},
abstract = {Linear systems with structures such as Toeplitz-, Vander\-mon
de- or Cauchy-likeness can be solved in $\tilde O (\alpha^2 n)$ operations, wher
e $n$ is the matrix size, $\alpha$ is its displacement rank, and $\tilde O (\,)$
denotes the omission of logarithmic factors. We show that for such matrices, th
is cost can be reduced to $\tilde O (\alpha^{\omega-1} n)$, where $\omega$ is a
feasible exponent for matrix multiplication over the base field. The best known
estimate for $\omega$ is $\omega < 2.38$, resulting in costs of order $\tilde O
(\alpha^{1.38} n)$. We present consequences for Hermite-Pad\'e approximation an
d bivariate interpolation.},
}
@inproceedings{BoKa09,
author = {Bostan, Alin and Kauers, Manuel},
title = {Automatic classification of restricted lattice walks},
booktitle = {DMTCS Proceedings of the 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'09), Hagenberg, Austria},
year = {2009},
pages = {203--217},
arxiv = {abs/0811.2899},
abstract = {We propose an experimental mathematics approach leading to the computer-driven discovery of various conjectures about structural properties of generating functions coming from enumeration of 2D and 3D lattice walks.},
}
@article{BoKa10,
author = {Bostan, Alin and Kauers, Manuel},
title = {The complete generating function for {G}essel walks is algebraic},
note = {With an Appendix by Mark van Hoeij},
journal = {Proceedings of the American Mathematical Society},
year = {2010},
volume = {138},
number = {9},
month = {September},
pages = {3063--3078},
arxiv = {abs/0909.1965},
abstract = {Gessel walks are lattice walks in the quarter plane $\set N^2$ which start at the origin~$(0,0)\in\set N^2$ and consist only of steps chosen from the set $\{\leftarrow,\penalty0\swarrow,\penalty0\nearrow,\penalty0\rightarrow\}$. We prove that if $g(n;i,j)$ denotes the number of Gessel walks of length~$n$ which end at the point~$(i,j)\in\set N^2$, then the trivariate generating series $\displaystyle\smash{ G(t;x,y)=\sum_{n,i,j\geq 0} g(n;i,j)x^i y^j t^n }$ is an algebraic function.},
}@incollection {BoLu09,
AUTHOR = {Bodini, Olivier and Lumbroso, J{\'e}r{\'e}mie},
TITLE = {Optimal partial tiling of {M}anhattan polyominoes},
BOOKTITLE = {Discrete geometry for computer imagery},
SERIES = {Lecture Notes in Comput. Sci.},
VOLUME = {5810},
PAGES = {79--91},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2009},
}
@article{BoMaPaRe06,
author = "V. Boeva and V. Makeev and D. Papatsenko and M. R{\'e}gnier",
title = "Short fuzzy tandem repeats in genomic sequences, identification, and possible role in regulation of gene expression",
year = "2006",
journal = {Bioinformatics},
volume = "22",
number = "6",
pages = "676--684"
}
@Inproceedings{BoMaRe04,
author = "V. Boeva and V. Makeev and M. R{\'e}gnier",
title = "{SWAN:} searching for highly divergent tandem repeats
in {DNA} sequences and statistical significance",
booktitle = "JOBIM'04",
publisher = "IEEE Computer Society",
year = "2004",
note = " In Proceedings JOBIM'04, Montr{\'e}al"
}
%% Created for Bruno Salvy at 2008-04-24 11:34:41 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{BoMoSaSc08,
Arxiv = {abs/cs/0609020},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Morain, Fran\c{c}ois and Salvy, Bruno and Schost, {\'E}ric},
Date-Added = {2006-09-06 15:46:06 +0200},
Date-Modified = {2008-04-24 11:34:36 +0200},
Doi = {10.1090/S0025-5718-08-02066-8},
Journal = {Mathematics of Computation},
Month = jul,
Number = {263},
Pages = {1755--1778},
Title = {Fast algorithms for computing isogenies between elliptic curves},
Volume = {77},
Year = {2008},
Abstract = {We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\ell$ ($\ell$ different from the characteristic) in time quasi-linear with respect to $\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\wp$-function and related functions.
},
Bdsk-Url-1 = {http://dx.doi.org/10.1090/S0025-5718-08-02066-8%20}}
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Bruno Salvy at 2008-08-04 15:08:44 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{BorweinSalvy2008,
Arxiv = {abs/0706.1409},
Author = {Borwein, Jonathan M. and Salvy, Bruno},
Date-Added = {2008-08-04 15:08:24 +0200},
Date-Modified = {2008-08-04 15:08:24 +0200},
Journal = {Experimental Mathematics},
Number = {2},
Pages = {223--230},
Title = {A proof of a recursion for {B}essel moments},
Volume = {17},
Year = {2008},
Abstract = {We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $K_0$.
},
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@inproceedings{BoSc09b,
author = {Bostan, Alin and Schost, {\'E}ric},
title = {Fast algorithms for differential equations in positive
characteristic},
booktitle = {ISSAC'09},
year = {2009},
editor = {May, John},
pages = {47--54},
doi = {10.1145/1576702.1576712},
arxiv = {abs/ 0901.3843},
abstract = {We address complexity issues for linear differential
equations in characteristic $p>0$: resolution and computation of the
$p$-curvature. For these tasks, our main focus is on algorithms whose
complexity behaves well with respect to $p$. We prove bounds linear in $p$ on
the degree of polynomial solutions and propose algorithms for testing the
existence of polynomial solutions in sublinear time $\tilde{O}(p^{1/2})$, and
for determining a whole basis of the solution space in quasi-linear time
$\tilde{O}(p)$; the $\tilde{O}$ notation indicates that we hide logarithmic
factors. We show that for equations of arbitrary order, the $p$-curvature can
be computed in subquadratic time $\tilde{O}(p^{1.79})$, and that this can be
improved to $O(\log(p))$ for first order equations and to $\tilde{O}(p)$ for
classes of second order equations.},
} @article{BoSc09,
author = {Bostan, Alin and Schost, {\'E}ric},
title = {A simple and fast algorithm for computing exponentials of power series},
journal = {Information Processing Letters},
year = {2009},
volume = {109},
number = {13},
pages = {754--756},
doi = {10.1016/j.ipl.2009.03.012},
abstract = {As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.},
}
@PhdThesis{Bostan03,
author = {Bostan, Alin},
title = {Algorithmique efficace pour des op{\'e}rations de base
en {C}alcul formel.},
school = {\'Ecole polytechnique},
type = {Th{\`e}se de Doctorat},
year = {2003},
url={http://algo.inria.fr/bostan/these/These.pdf},
abstract = {The subject of this thesis is the design
and implementation of efficient algorithms for some basic operations in
computer algebra, as well as their applications to related fields,
such as computational number theory and cryptography.
The first part of the text is dedicated to basic
algorithms on univariate polynomials. The tool which we use
systematically is a constructive version of Tellegen's transposition
principle, which makes it possible to obtain new algorithms for the
problems of multipoint evaluation and interpolation (in various
polynomial bases and for various families of evaluation points), as
well as a theorem of equivalence between the complexities of these two
problems.
The second part is devoted to fast computation with
algebraic numbers. We begin by studying certain elementary operations,
such as the composed sum and the composed product and their generalization
--- the diamond product of Brawley and~Carlitz. Their calculation rests
on the use of the formal Newton operator and the algebraic duality,
translated algorithmically by the use of transposition principle and
baby step / giant step methods. The results are then generalized to
the framework of zero-dimensional algebraic polynomial systems, for
the computation of minimal polynomials in quotient algebras and that
of rational parametrizations.
In the third part, we investigate the question of
the efficient computation of a term in a linear recurrent sequence
with polynomial coefficients. As an application, we obtain theoretical
and practical improvements of a point-counting method used in
hyperelliptic curve cryptography. Then, we propose an
evaluation-interpolation type method for certain usual operations on
linear differential operators with polynomial coefficients.}
}
@inproceedings {Bostan10,
AUTHOR = {Bostan, Alin},
TITLE = {Algorithmes rapides pour les polyn\^omes, s\'eries formelles et matrices},
BOOKTITLE = {Actes des Journ\'ees Nationales de Calcul Formel},
NOTE = {Les cours du CIRM, tome 1, num\'ero 2},
YEAR = {2010},
PAGES = {75--262},
ADDRESS = {Luminy, France},
URL = {http://ccirm.cedram.org:80/ccirm-bin/fitem?id=CCIRM_2010__1_2_75_0},
}
}
@article{BoSc05,
author = {A. Bostan and {\'E}. Schost},
title = {Polynomial evaluation and interpolation on special sets of
points},
journal = {Journal of Complexity},
number = {4},
year = {2005},
month = {August},
volume = {21},
pages = {420--446},
note = {Festschrift for the 70th Birthday of Arnold
Sch{\"o}nhage},
doi={10.1016/j.jco.2004.09.009},
abstract = {We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively, to computations with linear differential operators and to polynomial matrix multiplication.},
}
@inproceedings{BoGoPeSc05,
author = {Bostan, A. and Gonz{\'a}lez-Vega, L. and Perdry, H. and
Schost, {\'E}.},
title = {From {N}ewton sums to coefficients: complexity issues in
characteristic $p$},
booktitle = {MEGA'05},
year = {2005},
note = {Eighth International Symposium on Effective Methods in
Algebraic Geometry, Porto Conte, Alghero, Sardinia (Italy), May 27th -- June
1st},
abstract={We consider the following problem: given the first $d$ Newton sums
of a degree $d$ polynomial $P$, recover the coefficients of $P$. We
propose fast algorithms to perform this conversion for polynomials
over the $p$-adic ring $\Z_p$. As an application, we deduce a new
algorithm to compute the \emph{composed product} of polynomials over
the finite field $\F_p$, whose bit-complexity improves the known results
by a factor of $\,\log d$ in many cases.},
}
@article{BoSc04b,
author = {A. Bostan and {\'E}. Schost},
title = {On the complexities of multipoint evaluation and
interpolation},
journal = {Theoretical Computer Science},
number = {1--3},
year = {2004},
month = {December},
volume = {329},
pages = {223--235},
doi={10.1016/j.jco.2004.09.009},
abstract={We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively, to computations with linear differential operators and to polynomial matrix multiplication.},
}
@inproceedings{BoLeSc03,
author = {Bostan, A. and Lecerf, G. and Schost, {\'E}.},
title = {Tellegen's Principle Into Practice},
booktitle = {Symbolic and Algebraic Computation},
year = {2003},
editor = {J. R. Sendra},
publisher = {ACM Press},
pages = {37--44},
note = {Proceedings of ISSAC'03, Philadelphia, August 2003.},
doi = {10.1145/860854.860870},
abstract = {The transposition principle, also called Tellegen's principle, is a set of transformation rules for linear programs. Yet, though well known, it is not used systematically, and few practical implementations rely on it. In this article, we propose explicit transposed versions of polynomial multiplication and division but also new faster algorithms for multipoint evaluation, interpolation and their transposes. We report on their implementation in Shoup's NTL C++ library.},
}
@InProceedings{BoGaSc03,
author = {A. Bostan and P. Gaudry and {\'E}. Schost},
title = {Linear recurrences with polynomial coefficients and
computation of the {C}artier-{M}anin operator on hyperelliptic curves},
booktitle = {Fq7, International Conference on Finite Fields and Applications
(Toulouse, France, May 5-9, 2003)},
pages = {40--58},
year = {2004},
editor = {Gary L. Mullen, Alain Poli, Henning Stichtenoth},
publisher = {Springer--Verlag},
series = {Lecture Notes in Computer Science},
volume = {2948},
doi={10.1007/b95905},
abstract = {We improve an algorithm originally due to Chudnovsky and Chudnovsky
for computing one selected term in a linear recurrent sequence with
polynomial coefficients. Using baby-steps / giant-steps techniques,
the $n$th term in such a sequence can be computed in time
proportional to $\sqrt{n}$, instead of $n$ for a naive approach.
As an intermediate result, we give a fast algorithm for computing the
values taken by an univariate polynomial $P$ on an arithmetic
progression, taking as input the values of $P$ on a translate on this
progression.
We apply these results to the computation of the Cartier-Manin
operator of a hyperelliptic curve. If the base field has
characteristic $p$, this enables us to reduce the complexity of this
computation by a factor of order $\sqrt{p}$. We treat a practical
example, where the base field is an extension of degree 3 of the
prime field with $p=2^{32}-5$ elements.},
}
@Article{Bostan-2011-EFG,
author = {Bostan, Alin and Chyzak, Frédéric and van Hoeij, Mark and Pech, Lucien},
title = {Explicit formula for the generating series of diagonal {3D} rook paths},
journal = {Sém. Loth. Comb.},
fjournal = {Séminaire Lotharingien de Combinatoire},
year = {2011},
OPTkey = {},
volume = {B66a},
OPTnumber = {},
OPTpages = {},
OPTmonth = {},
note = {27 pages},
OPTannote = {},
url = {http://www.emis.de/journals/SLC/wpapers/s66bochhope.html},
abstract = {Let $a_n$ denote the number of ways in which a chess rook can move from a
corner cell to the opposite corner cell of an $n \times n \times n$
three-dimensional chessboard, assuming that the piece moves closer to the goal
cell at each step. We describe the computer-driven \emph{discovery and
proof\/} of the fact that the generating series $G(x)= \sum_{n \geq 0}
a_n x^n$ admits the following explicit expression in terms of a Gaussian hypergeometric function:
\[
G(x) = 1 + 6 \cdot \int_0^x \frac{ \,\pFq21{1/3}{2/3}{2}
{\frac{27 w(2-3w)}{(1-4w)^3}}}{(1-4w)(1-64w)} \, dw.
\]}
}
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Bruno Salvy at 2008-08-04 15:42:35 +0200
%% Saved with string encoding Unicode (UTF-8)
@inproceedings{BostanSalvySchost2008,
Arxiv = {abs/0804.2337},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Salvy, Bruno and Schost, {\'E}ric},
Booktitle = {ISSAC'08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation},
Date-Added = {2008-02-08 16:29:54 +0100},
Date-Modified = {2008-08-04 15:42:35 +0200},
Doi = {10.1145/1390768.1390806},
Editor = {Jeffrey, David J.},
Pages = {269--276},
Publisher = {ACM Press},
Title = {Power Series Composition and Change of Basis},
Year = {2008},
Abstract = {Efficient algorithms are known for many operations on truncated power
series (multiplication, powering, exponential,...). Composition is
a more complex task. We isolate a large class of power series for
which composition can be performed efficiently. We deduce fast
algorithms for converting polynomials between various bases, including
Euler, Bernoulli, Fibonacci, and the orthogonal Laguerre, Hermite,
Jacobi, Krawtchouk, Meixner and Meixner-Pollaczek.
},
Bdsk-Url-1 = {http://dx.doi.org/10.1145/1390768.1390806}}
@article{BostanSalvySchost2010,
Arxiv = {abs/0804.2373},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Salvy, Bruno and Schost, {\'E}ric},
Date-Added = {2008-04-14 21:02:29 -0300},
Date-Modified = {2009-11-19 08:17:36 +0100},
Doi = {10.1016/j.laa.2009.08.002},
Journal = {Linear Algebra and its Applications},
Month = jan,
Number = {1},
Pages = {249--258},
Title = {Fast conversion algorithms for orthogonal polynomials},
Volume = {432},
Year = {2010},
Abstract = {We discuss efficient conversion algorithms for orthogonal polynomials. We describe
a known conversion algorithm from an arbitrary orthogonal basis to the monomial
basis, and deduce a new algorithm of the same complexity for the converse operation.
}
}
@article{BostanSalvyTran2010,
Arxiv = {abs/0907.0291},
Author = {Bostan, Alin and Salvy, Bruno and Tran, Khang},
Date-Added = {2009-07-03 16:01:28 +0200},
Date-Modified = {2010-11-30 07:49:35 +0100},
Doi = {10.1142/S1793042110003691},
Journal = {International Journal of Number Theory},
Number = {7},
Pages = {1659--1667},
Title = {Generating functions of {C}hebyshev-like polynomials},
Volume = {6},
Year = {2010},
Abstract = {In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.
}
}
@InProceedings{BrCaDu03,
author = "Herv\'e Br{\"o}nnimann and Fr\'ed\'eric Cazals and
Marianne Durand",
title = "Randomized Jumplists: A Jump-and-Walk Dictionary DataStructure",
year = "2003",
booktitle = "Proceedings of the STACS'03 Conference, Berlin,
February 2003",
volume= 2607,
pages = "283--294",
series = "Lecture Notes in Computer Science",
publisher = "Springer Verlag"
}
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Nicolas Broutin at 2012-02-07 20:20:46 -0700
%% Saved with string encoding Unicode (UTF-8)
@unpublished{BrNeSu2012b,
Arxiv = {abs/1202.1342},
Author = {Broutin, N. and Neininger, R. and Sulzbach, H.},
Date-Added = {2012-02-07 10:54:54 +0000},
Date-Modified = {2012-02-08 03:20:46 +0000},
Keywords = {partial match},
Note = {Submitted},
Title = {{A limit process for partial match queries in random quadtrees}},
Year = {2012}}
@unpublished{AdBrHo2011a,
Arxiv = {abs/1110.6455},
Author = {Addario-Berry, L. and Broutin, N. and Holmgren, C.},
Date-Added = {2011-10-29 10:59:42 +0200},
Date-Modified = {2011-11-02 07:45:24 +0100},
Note = {Submitted},
Title = {{Cutting down trees with a Markov chainsaw}},
Year = {2011}}
@unpublished{BrMa2011a,
Arxiv = {abs/1110.5203},
Author = {Broutin, N. and Marckert, J.-F.},
Date-Added = {2011-10-25 06:51:39 +0200},
Date-Modified = {2011-10-25 06:53:25 +0200},
Keywords = {CRT, random tree},
Note = {Submitted},
Title = {{Asymptotic of trees with a prescribed degree sequence and applications}},
Year = {2011}}
@inproceedings{BrNeSu2012a,
Arxiv = {abs/1107.2231},
Author = {Broutin, N. and Neininger, R. and Sulzbach, H.},
Booktitle = {Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA)},
Date-Added = {2011-07-12 13:20:59 +0200},
Date-Modified = {2012-01-20 10:12:33 +0000},
Editor = {Rabani, Y.},
Keywords = {partial match},
Pages = {1056--1065},
Title = {{Partial match queries in random quadtrees}},
Year = {2012}}
@unpublished{BrDeFrLu2011a,
Arxiv = {abs/1103.0351},
Author = {Broutin, N. and Devroye, L. and Fraiman, N. and Lugosi, G.},
Date-Added = {2011-03-01 16:32:59 +0100},
Date-Modified = {2011-03-03 07:39:34 +0100},
Keywords = {geometric graph, network, Bluetooth},
Note = {Submitted},
Title = {{Connectivity threshold for Bluetooth graphs}},
Year = {2011}}
@article{BrHo2011a,
Arxiv = {abs/1102.2541},
Author = {Broutin, N. and Holmgren, C.},
Date-Added = {2011-02-12 10:40:42 +0100},
Date-Modified = {2011-05-18 11:52:45 +0200},
Journal = {The Annals of Applied Probability},
Keywords = {path length, random tree},
Title = {{The total path length of split trees}},
Year = {To appear}}
@unpublished{BrFa2011a,
Arxiv = {abs/1101.5547},
Author = {Broutin, N. and Fawzi, O.},
Date-Added = {2011-01-28 11:16:27 +0100},
Date-Modified = {2011-01-31 08:52:13 +0100},
Note = {Submitted},
Title = {{Longest distance in random circuits}},
Year = {2011}}
@article{BrFl2010,
Arxiv = {abs/1009.1515},
Author = {Broutin, N. and Flajolet, P.},
Date-Added = {2010-09-09 13:53:29 +0200},
Date-Modified = {2011-05-18 11:53:10 +0200},
Journal = {Random Structures and Algorithms},
Keywords = {height, diameter, random tree},
Title = {{The distribution of height and diameter in random non-plane binary trees}},
Year = {To appear}}
@inproceedings{AdBrRe2006,
Author = {Addario-Berry, L. and Broutin, N. and Reed, B.},
Booktitle = {Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees Combinatorics and Probability},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-28 10:32:46 +0100},
Keywords = {random tree, random walk, diameter, MST},
Pages = {237--240},
Publisher = {Discrete Mathematics and Theoretical Computer Science},
Series = {DMTCS Proceedings},
Title = {The diameter of the minimum spanning tree of the complete graph},
Url = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAG0116},
Volume = {AG},
Year = {2006},
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Bdsk-Url-1 = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAG0116}}
@article{BrDeMc2010,
Author = {Broutin, N. and Devroye, L. and McLeish, E.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2011-05-18 11:52:19 +0200},
Journal = {Algorithmica},
Keywords = {mst, height, tree, euclidean, percolation},
Pages = {141--156},
Title = {{Note on the structure of Kruskal's algorithm}},
Volume = {56},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00453-008-9164-4}}
@article{BrDe2006,
Author = {Broutin, N. and Devroye, L.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-27 09:07:59 +0100},
Doi = {10.1007/s00453-006-0112-x},
Journal = {Algorithmica},
Keywords = {weighted tree, large deviation, branching random walk},
Pages = {271--297},
Title = {{Large deviations for the weighted height of an extended class of trees}},
Volume = {46},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00453-006-0112-x}}
@inproceedings{BrDe2007,
Author = {Broutin, N. and Devroye, L.},
Booktitle = {International Conference on Analysis of Algorithms},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-28 10:32:03 +0100},
Keywords = {trie, TST, profile, height},
Pages = {271--282},
Publisher = {Discrete Mathematics and Theoretical Computer Science},
Series = {DMTCS Proceedings},
Title = {The height of list tries and {TST}},
Url = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAH0118},
Volume = {AH},
Year = {2007},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAH0118}}
@article{BrDe2008a,
Author = {Broutin, N. and Devroye, L.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-27 09:09:00 +0100},
Doi = {10.1017/S0963548307008796},
Journal = {Combinatorics, Probability and Computing},
Keywords = {trie, height},
Pages = {161--202},
Title = {{An analysis of the height of tries with random weights on the edges}},
Volume = {17},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0963548307008796}}
@article{BrDeMc2008,
Author = {Broutin, N. and Devroye, L. and McLeish, E.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-27 09:09:29 +0100},
Doi = {10.1007/s00236-008-0069-0},
Journal = {Acta Informatica},
Keywords = {random tree, height, large deviation},
Pages = {237--277},
Title = {Weighted height of random trees},
Volume = {45},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00236-008-0069-0}}
@inproceedings{BrFl2008,
Author = {Broutin, N. and Flajolet, P.},
Booktitle = {Fifth Colloquium on Mathematics and Computer Science},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-28 10:30:45 +0100},
Keywords = {height},
Pages = {121--134},
Series = {DMTCS Proceedings},
Title = {The height of random binary unlabelled trees},
Url = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAI0106},
Volume = {AI},
Year = {2008},
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Bdsk-Url-1 = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAI0106}}
@article{BrDeMcSa2008,
Author = {Broutin, N. and Devroye, L. and McLeish, E. and de la Salle, M.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2011-03-01 16:45:44 +0100},
Doi = {10.1002/rsa.20202},
Journal = {Random Structures and Algorithms},
Keywords = {increasing trees, height},
Pages = {494--518},
Title = {The height of increasing trees},
Volume = {32},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.20202}}
@article{AdBrLu2010,
Author = {Addario-Berry, L. and Broutin, N. and Lugosi, G.},
Bdsk-Url = {http://dx.doi.org/10.1017/S0963548309990204},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-12-05 10:26:09 +0100},
Doi = {10.1017/S0963548309990204},
Journal = {Combinatorics, Probability and Computing},
Keywords = {recursive tree, random graph},
Pages = {1--19},
Title = {The longest minimum weight path in a complete graph},
Volume = {19},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0963548309990204}}
@article{AdBrDeLu2010,
Arxiv = {abs/0908.3437},
Author = {Addario-Berry, L. and Broutin, N. and Devroye, L. and Lugosi, G.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2011-05-18 11:52:19 +0200},
Journal = {The Annals of Statistics},
Keywords = {statistics},
Pages = {3063--3092},
Title = {On combinatorial testing problems},
Volume = {38},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1214/10-AOS817}}
@article{AdBrRe2009,
Author = {Addario-Berry, L. and Broutin, N. and Reed, B.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-27 09:13:01 +0100},
Doi = {10.1002/rsa.20241},
Journal = {Random Structures Algorithms},
Keywords = {diameter, random walk, MST},
Pages = {323--347},
Title = {Critical random graphs and the structure of a minimum spanning tree},
Volume = {35},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.20241}}
@article{AdBrGo2010,
Arxiv = {abs/0908.3629},
Author = {Addario-Berry, L. and Broutin, N. and Goldschmidt, C.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2010-05-24 23:05:17 +0200},
Journal = {Electronic Journal of Probability},
Keywords = {random graph, CRT},
Pages = {741--775},
Title = {Critical random graphs: limiting constructions and distributional properties},
Volume = {15},
Year = {2010}}
@article{AdBr2010,
Arxiv = {abs/0908.1083},
Author = {Addario-Berry, L. and Broutin, N.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2011-05-18 11:52:19 +0200},
Journal = {Probability Theory and Related Fields},
Keywords = {branching random walk, large deviation},
Title = {Total progeny in killed branching random walk},
Year = {To appear},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00440-010-0299-2}}
@article{AdBrLu2009,
Arxiv = {abs/0801.1909},
Author = {Addario-Berry, L. and Broutin, N. and Lugosi, G.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2009-11-28 10:34:00 +0100},
Doi = {10.1214/08-AAP572},
Journal = {The Annals of Applied Probability},
Keywords = {branching process, resistance},
Pages = {1092--1107},
Title = {Effective resistance of random trees},
Volume = {19},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1214/08-AAP572}}
@article{AdBrGo2010a,
Arxiv = {abs/0903.4730},
Author = {Addario-Berry, L. and Broutin, N. and Goldschmidt, C.},
Date-Added = {2009-11-23 15:25:01 +0100},
Date-Modified = {2011-03-04 08:44:58 -0500},
Doi = {10.1007/s00440-010-0325-4},
Journal = {Probability Theory and Related Fields},
Keywords = {scaling limit, CRT, Brownian, random graph, diameter},
Title = {{The continuum limit of critical random graphs}},
Year = {To appear},
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%% Created for Bruno Salvy at 2008-04-24 11:37:03 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{ChDrKlKo07,
Arxiv = {abs/cs/0605019},
Author = {Chyzak, Fr{\'e}d{\'e}ric and Drmota, Michael and Klausner, Thomas and Kok, Gerard},
Date-Modified = {2008-04-24 11:37:03 +0200},
Doi = {10.1017/S0963548307008425},
Journal = {Combinatorics, Probability \& Computing},
Title = {The distribution of patterns in random trees},
Web-Comment = {The 2004 version of this paper was incomplete and removed from this list.},
Year = {2008},
volume = 17,
pages = {21--59},
Abstract = {Let~$T_n$ denote the set of unrooted labeled trees of size~$n$ and let~$M$ be a particular (finite, unlabeled) tree. Assuming that every tree of~$T_n$ is equally likely, it is shown that the limiting distribution as $n$~goes to infinity of the number of occurrences of~$M$ as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to $\mu n$ and~$\sigma^2n$, respectively, where the constants $\mu>0$ and~$\sigma\ge 0$ are computable.},
Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0963548307008425}}
@misc{ChLi90,
author = "Chen, Shaoshi and Li, Ziming",
title = "A speed-up of the {H}ermite reduction for rational functions",
howpublished = "Poster at the conference ICMM'09 (Beijing, China)",
year = 2009,
url = {http://mmrc.iss.ac.cn/wu90/}
}
@misc{BoChChLi09,
author = "Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Chen, Shaoshi and Li, Ziming",
title = "Rational-functions telescopers: {B}lending creative telescoping with {H}ermite reduction",
howpublished = "Poster at the conference ISSAC'09 (Seoul, South Korea)",
year = 2009,
url = {http://issac2009.kias.re.kr/program_page.html#posters}
}
@PhdThesis{Chen2011,
author = {Chen, Shaoshi},
title = {Quelques applications de l'algčbre différentielle et aux différences pour le télescopage créatif},
school = {École polytechnique (Palaiseau, France)},
year = {2011},
OPTkey = {},
type = {Ph{D} thesis},
OPTaddress = {},
month = feb,
note = {Defended on February 16, 2011},
OPTannote = {},
url = {http://algo.inria.fr/papers/pdf/Chen-2011-SAD.pdf},
abstract = {Since the 1990's, Zeilberger's method of
creative telescoping has played an important role in the automatic
verification of special-function identities. The long-term goal initiated
in this work is to obtain fast algorithms and implementations for
definite integration and summation in the framework of this method.
Our contributions include new practical algorithms, complexity
analyses of algorithms, and theoretical criteria for the termination of existing
algorithms.
On the practical side, we present a new algorithm for computing minimal
telescopers for bivariate rational functions.
This algorithm is based on Hermite reduction.
We also improve the classical Almkvist and Zeilberger's
algorithm for rational-function inputs.
The Hermite-reduction based algorithm and
improved Almkvist and Zeilberger's algorithm are
analyzed in terms of field operations.
Both complexity analysis and experimental results
show that our algorithms are superior to other known
ones for rational-function inputs.
On the theoretic side, we present a structure theorem for multivariate
hyperexponential-hypergeometric functions. This theorem is based on
(multivariate) Christoper's theorem for hyperexponential functions,
the Ore-Sato theorem for hypergeometric terms, and our generalization
of a recent result by Feng, Singer, and Wu
on compatible bivariate continuous-discrete rational functions.
The structure theorem allows us to decomposes a
hyperexponential-hypergeometric function as a product of a rational function,
several exponential and power functions, and factorial terms.
Furthermore, we derive two criteria for
the existence of telescopers for bivariate hyperexponential-hypergeometric functions:
one is with respect to the continuous variable, and the other with respect to the discrete one.
The two criteria solve the termination problems of the continuous-discrete analogue
of Zeilberger's algorithms.}
}
@Article{ChFl01,
title = "Hachage, Arbres, Chemins, et Graphes",
author = "Philippe Chassaing and Philippe Flajolet",
journal = "Bulletin de Probabilit\'es",
volume = 5,
address = "Universit\'e Paris VI",
year = 2001,
pages = "1--17"
}
@Article{ChFl03,
title = "Hachage, Arbres, Chemins, et Graphes",
author = "Philippe Chassaing and Philippe Flajolet",
journal = "Gazette des Math\'ematiciens",
address = "Soci\'et\'e Math\'ematique de France",
year = 2003,
pages = "29--49"
}
@Article{ChFlGaGi04,
author = "Brigitte Chauvin and Philippe Flajolet and Dani\`ele Gardy
and Bernhard Gittenberger",
title = "{And/Or Trees Revisited}",
year = 2004,
journal = "Combinatorics, Probability and Computing",
volume = 13,
number = "4--5",
pages = "501--513",
note = "Special issue on Analysis of Algorithms.",
}
@Book{ChFlGaMo02,
editor ="Brigitte Chauvin and Philippe Flajolet
and Dani\`ele Gardy and A. Mokkadem",
title = {Mathematics and Computer Science II:
Algorithms, Trees, Combinatorics and Probabilities},
isbn = "ISBN 3-7643-6933-7",
publisher = "{Birkh\"auser Verlag}",
address = "Basel",
year = 2002,
series = "Trends in Mathematics",
note = "560 pages. Proceedings of a
Colloquium held at Versailles, September 2002"
}
@inproceedings {ChFlGoLe09,
AUTHOR = {Cheung, Y. K. and Flajolet, P. and Golin, M. and Lee, C. Y. J.},
TITLE = {Multidimensional Divide-and-Conquer and Weighted Digital Sums (Extended Abstract)},
BOOKTITLE = {Proceedings of the Fifth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)},
PAGES = {58--65},
PUBLISHER = {SIAM Press},
YEAR = {2009},
}
@Article{ChGuPa99,
author = {Chyzak, Fr{\'e}d{\'e}ric and Gutman, Ivan and Paule, Peter},
title = {Predicting the Number of Hexagonal Systems with 24 and~25
Hexagons},
journal = {Communications in Mathematical and Computer Chemistry},
year = 1999,
volume = 40,
pages = {139--151},
Web-comment = {Preliminary version.},
Abstract = {We predict the number of hexagonal systems consisting of 24 and~25
hexa\-gons to be $H_{24}=122237774262384$
and~$H_{25}=606259305418149$, with 6 and~5 significant digits,
respectively. Further estimates for~$H_n$ up to~${n=31}$ are also
given.}
}
@Article{ChKaSo89,
author = "Christine Choppy and St{\'e}phane Kaplan and
Mich{\`e}le Soria",
title = "Complexity analysis of Term Rewriting Systems",
journal = "Theoretical Computer Science",
year = 1989,
volume = "67",
pages = "261--282"
}
@inproceedings{ChMiSa02,
Address = {Melbourne, Australia},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Chyzak, Fr\'ed\'eric and Mishna, Marni and Salvy, Bruno},
Booktitle = {14th Conference of Formal Power Series and Algebraic Combinatorics},
Month = jul,
Note = {Extended abstract. Proceedings FPSAC'02. An extended version has appeared in~\cite{ChMiSa05}},
Pages = {19.1--19.12},
Publisher = {University of Melbourne},
Title = {Effective {D}-finite Symmetric Functions},
Year = 2002,
Web-comment = {Preliminary version.},
Abstract = {Many combinatorial generating functions can be extracted from
symmetric functions. Gessel has outlined a large class of symmetric
functions for which the resulting generating functions are D-finite.
We extend Gessel's work by providing algorithms that compute
differential equations these generating functions satisfy. Examples
of applications to $k$-regular graphs and Young tableaux with
repeated entries are given.}
}
@InCollection{ChPa05,
author = {Chyzak, Frédéric and Paule, Peter},
title = {Computer algebra},
booktitle = {Digital Library of Mathematical Functions},
year = {2005},
editor = {Lozier, Dan and Olver, Frank and Clark, Charles and Boisvert, Ron},
publisher = {NIST},
note = {40~pages. Under the process of validation by NIST},
Web-comment = {This ambitious project, DLMF, is managed by NIST and aims at providing a new edition for the Handbook of Mathematical Functions,
an authoritative handbook since 1962.},
Abstract = {This chapter focuses on computer algebra techniques which are tailored primarily for special function applications, that is, for symbolic manipulation of expressions representing special functions and sequences. The described methods are algorithms rather than formulas or identities.},
}
@article {ChPaScScZi01,
AUTHOR = {Chyzak, Fr{\'e}d{\'e}ric and Paule, Peter and Scherzer, Otmar
and Schoisswohl, Armin and Zimmermann, Burkhard},
TITLE = {The construction of orthonormal wavelets using symbolic
methods and a matrix analytical approach for wavelets on the
interval},
JOURNAL = {Experimental Mathematics},
VOLUME = {10},
YEAR = {2001},
NUMBER = {1},
PAGES = {67--86},
Web-comment = {Preliminary version.},
Abstract = {In this paper we discuss closed form representations of filter
coefficients of wavelets on the real line, half real line and on
compact intervals. We show that computer algebra can be applied to
achieve this task. Moreover, we present a matrix analytical approach
that unifies constructions of wavelets on the interval.}
}
@inproceedings{ChQuRo03,
author = {Chyzak, Fr\'ed\'eric and Quadrat, Alban and Robertz, Daniel},
title = {Linear control systems over {O}re algebras: effective algorithms for the computation of parametrizations},
booktitle = {Time-Delay Systems},
note = {Electronic proceedings of an IFAC Workshop, INRIA-Roquencourt (France)},
year = 2003,
Url = {http://algo.inria.fr/chyzak/Publications/tds03.ps},
Web-comment = {Conference web site.}
}
@InProceedings{ChQuRo04,
author = "Fr\'ed\'eric Chyzak and Alban Quadrat and Daniel Robertz",
title = "{OreModules}, A symbolic package for the study of multidimensional linear systems",
booktitle = "Sixteenth International Symposium on Mathematical Theory of Networks and Systems",
publisher = "Katholieke Universiteit Leuven",
address = "Leuven, Belgium",
month =jul,
year = 2004,
note = "Proceedings MTNS2004, Katholieke Universiteit Leuven, Belgium, July 5--9, 2004",
Url = {http://www.mtns2004.be/database/papersubmission/upload/206.pdf},
Web-comment = {More on the package web site.}
}
@Article{ChQuRo05,
author = {Chyzak, Fr{\'e}d{\'e}ric and Quadrat, Alban and Robertz, Daniel},
title = {Effective algorithms for parametrizing linear control systems over {O}re algebras},
journal = {Applicable Algebra in Engineering, Communication and Computing},
publisher = "Springer Verlag",
year = 2005,
month = nov,
volume = 16,
number = 5,
pages = {319--376},
Doi = {10.1007/s00200-005-0188-6},
Web-comment = {Preliminary version (INRIA Research Report #5181).},
Abstract = {In this paper, we study linear control systems over Ore algebras.
Within this mathematical framework, we can
simultaneously deal
with different classes of linear control systems such as time-varying ordinary
differential systems (ODEs),
differential time-delay systems, partial differential equations (PDEs), multidi
mensional discrete systems,
multidimensional codes etc.
We give effective algorithms which check whether or not
a linear control system over some Ore algebra is controllable, parametrizable,
flat or $\pi$-free.}
}
@InProceedings{ChQuRo07,
author = {Chyzak, Fr\'ed\'eric and Quadrat, Alban and Robertz, Daniel},
title = {{OreModules}: A symbolic package for the study of multidimensional linear systems},
booktitle = {Applications of Time Delay Systems},
publisher = {Springer Berlin / Heidelberg},
editor = {Chiasson, J. and Loiseau, J. J.},
year = 2007,
volume = 352,
series = {Lecture Notes in Control and Information Sciences},
pages = {233--264},
note = {ISBN 978-3-540-49555-0},
Doi = {10.1007/978-3-540-49556-7_15},
Abstract = {In the seventies, the study of transfer matrices of time-invariant linear systems of ordinary differential equations (ODEs) led to the development of the polynomial approach. In particular, the univariate polynomial matrices play a central role in this approach (e.g., Hermite, Smith and Popov forms, invariant factors, primeness, B\'ezout/Diophantine equations).}
}
@article{ChSa98,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Chyzak, Fr{\'e}d{\'e}ric and Salvy, Bruno},
Doi = {10.1006/jsco.1998.0207},
Journal = {Journal of Symbolic Computation},
Month = aug,
Number = 2,
Pages = {187--227},
Title = {Non-commutative Elimination in {O}re Algebras Proves Multivariate Holonomic Identities},
Volume = 26,
Year = 1998,
Web-comment = {See the accompanying Maple session and the errata.},
Abstract = {Many computations involving special functions, combinatorial sequences or theirq-analogues can be performed using linear operators and simple arguments on the dimension of related vector spaces. In this article, we develop a theory of -finite sequences and functions which provides a unified framework to express algorithms for computing sums and integrals and for the proof or discovery of multivariate identities. This approach is vindicated by an implementation.}
}
@TechReport{Chyzak00a,
author = {Chyzak, Fr{\'e}d{\'e}ric},
title = {About the non-minimality of the outputs
of {Z}eilberger's algorithm},
institution = {Austrian project SFB F013},
year = {2000},
type = {Numerical and Symbolic Scientific Computing,
Research Report},
number = {00-08},
address = {Linz, Austria},
month = {avril},
note = {Bruno Buchberger and Peter Paule, Eds. 20 pages},
Url = {http://www.sfb013.uni-linz.ac.at/reports/2000/ps-files/sfb00-08.ps.gz},
Web-comment = {This work is still at a preliminary stage and needs more thoughts...},
Abstract = {We report on case studies where Zeilberger's fast algorithm and the
other holonomy-based algorithms known so far for definite
hypergeometric summation fail to find the minimal annihilating
recurrence satisfied by the sum. To explain the phenomenon we propose
a new elimination paradigm, together with a promising heuristic method
which we hope to turn into an algorithm in the future. The approach
applies to $\partial$-finite functions as well and extends to the
related algorithms.}
}
@Article{Chyzak00b,
author = {Fr{\'e}d{\'e}ric Chyzak},
title = {An Extension of {Z}eilberger's Fast Algorithm to
General Holonomic Functions},
journal = {Discrete Mathematics},
year = 2000,
volume = 217,
number = {1-3},
pages = {115--134},
note = {Special issue Formal power series and algebraic combinatorics (Vienna, 1997)},
url = {http://www.inria.fr/rrrt/rr-3195.html},
Web-comment = {Preliminary version (INRIA Research Report #3195).},
Abstract = {\emph{(English)}
We extend Zeilberger's fast algorithm for definite
hypergeometric summation to non-hypergeometric holonomic sequences.
The algorithm generalizes to the differential case and to~$q$-calculus
as well. Its theoretical justification is based on a description by
linear operators and on the theory of holonomy.
\emph{(French)}
Nous \'etendons l'algorithme rapide de
Zeilberger pour la sommation hyper\-g\'eo\-m\'e\-trique d\'efinie au
cas des suites holonomes non hyperg\'eo\-m\'e\-triques.
L'algo\-rithme se g\'en\'era\-li\-se aussi au cas diff\'erentiel et
du~$q$-calcul. Sa justification th\'eorique se fonde sur une
description par op\'erateurs lin\'eaires et sur la th\'eorie de
l'holonomie.}
}
@proceedings{Chyzak00c,
title = {Algorithms Seminar, 1999--2000},
year = 2000,
editor = {Chyzak, Fr{\'e}d{\'e}ric},
volume = 4056,
series = {Research Report},
month = nov,
organization = {Institut National de Recherche en Informatique et en
Automatique},
url = {http://www.inria.fr/rrrt/rr-4056.html},
Abstract = {These seminar notes constitute the proceedings of a
seminar devoted to the analysis of algorithms and related topics. The
subjects covered include combinatorics, symbolic computation,
asymptotic analysis, computational biology, and average-case analysis
of algorithms and data structures.}
}
@proceedings{Chyzak02,
title = {Algorithms Seminar, 2000--2001},
year = 2002,
editor = {Chyzak, Fr{\'e}d{\'e}ric},
volume = 4406,
series = {Research Report},
month = mar,
organization = {Institut National de Recherche en Informatique et en
Automatique},
url = {http://www.inria.fr/rrrt/rr-4406.html},
Abstract = {These seminar notes constitute the proceedings of a
seminar devoted to the analysis of algorithms and related topics. The
subjects covered include combinatorics, symbolic computation,
asymptotic analysis, computational biology, and average-case analysis
of algorithms and data structures.}
}
@proceedings{Chyzak03,
title = {Algorithms Seminar, 2001--2002},
year = 2003,
editor = {Chyzak, Fr{\'e}d{\'e}ric},
volume = 5003,
series = {Research Report},
month = nov,
organization = {Institut National de Recherche en Informatique et en
Automatique},
url = {http://www.inria.fr/rrrt/rr-5003.html},
Abstract = {These seminar notes constitute the proceedings of a
seminar devoted to the analysis of algorithms and related topics. The
subjects covered include combinatorics, symbolic computation,
asymptotic analysis, number theory, as well as the analysis of
algorithms, data structures, and network protocols.}
}
@proceedings{Chyzak05,
title = {Algorithms Seminar, 2002--2004},
year = 2005,
editor = {Chyzak, Fr{\'e}d{\'e}ric},
volume = 5542,
series = {Research Report},
month = apr,
organization = {Institut National de Recherche en Informatique et en
Automatique},
note = {120 pages},
Abstract = {These seminar notes constitute the proceedings of a
seminar devoted to the analysis of algorithms and related topics. The
subjects covered include combinatorics, symbolic computation, and the
asymptotic analysis of algorithms, data structures, and network
protocols.}
}
@TechReport{Chyzak94,
author = {Fr{\'e}d{\'e}ric Chyzak},
title = {Holonomic Systems and Automatic Proofs of Identities},
institution = {Institut National de Recherche en Informatique et en
Automatique},
year = 1994,
month = oct,
type = {Research Report},
number = 2371,
url = {http://www.inria.fr/rrrt/rr-2371.html},
Abstract = {This report presents three computer algebra packages in the Maple language
for the symbolic manipulation of linear systems of differential and recurrence
equations.
They are especially designed to deal with so-called holonomic systems.
We also give a theoretical justification to our implementation.
The set of holonomic functions and sequences is a large class of objects.
It forms an algebra and is closed under algebraic substitution and diagonal.
An implementation of these properties makes it possible to perform computer
assisted proofs of holonomic identities in a simple way, since any holonomic
system has a normal form obtained by an extension of the Gröbner basis
algorithm.
For instance, combinatorial problems often lead to holonomic systems and to
identities involving binomial coefficients.
Many identities involving special functions are also captured by the theory of
holonomy.
Examples are given to show how some interesting identities are proved by our
system.}
}
@InProceedings{Chyzak97,
author = {Chyzak, Fr{\'e}d{\'e}ric},
title = {An Extension of {Z}eilberger's Fast Algorithm to General Holonomic Functions},
booktitle = {Formal Power Series and Algebraic Combinatorics, 9th Conference},
pages = {172--183},
year = 1997,
organization = {Universit{\"a}t Wien},
note = {Conference proceedings. Subsumed in~\cite{Chyzak00b}},
Web-comment = {Preliminary version (INRIA Research Report #3195).}
}
@InCollection{Chyzak98b,
author = {Fr{\'e}d{\'e}ric Chyzak},
title = {Gr{\"o}bner Bases, Symbolic Summation and Symbolic
Integration},
booktitle = {Gr{\"o}bner Bases and Applications},
publisher = {Cambridge University Press},
year = 1998,
editor = {B. Buchberger and F. Winkler},
volume = 251,
series = {London Mathematical Society Lecture Notes Series},
pages = {32--60},
note = {Proceedings of the Conference
33 Years of Gr\"obner Bases, ISBN 0-521-63298-6},
Web-comment = {Preliminary version (INRIA Research Report #3297). Errata.},
Abstract = {The treatment of combinatorial expressions and
special functions by linear operators is amenable to Gr\"obner basis
methods. In this tutorial, we illustrate the applications of
Gr\"obner bases to symbolic summation and integration.}
}
@PhdThesis{Chyzak98,
author = {Fr{\'e}d{\'e}ric Chyzak},
title = {Fonctions holonomes en calcul formel},
school = {{\'E}cole polytechnique},
year = 1998,
type = {Th{\`e}se de Doctorat},
note = {INRIA, TU~0531. 227~pages.},
url = {http://algo.inria.fr/chyzak/Publications/these.ps},
Abstract = {\emph{(French)} Cette th\`ese montre comment le calcul formel
permet la manipulation d'une grande classe de suites et fonctions
solutions d'op\'erateurs lin\'eaires, la classe des fonctions
holonomes. Celle-ci contient de nombreuses fonctions sp\'eciales, en
une ou plusieurs variables, et de nombreuses suites de la
combinatoire. Un cadre th\'eorique est tout d'abord introduit pour
algorithmiser les propri\'et\'es de cl\^oture de la classe holonome,
pour y per\-met\-tre un test \`a z\'ero et pour unifier les calculs
diff\'erentiels sur les fonctions et les calculs de r\'ecurrences sur
les suites. Ces m\'ethodes s'appuient sur des calculs par une
extension de la th\'eorie des bases de Gr\"obner dans un cadre de
polyn\^omes non commutatifs, les polyn\^omes de Ore. Deux types
d'algorithmes de sommation et d'int\'egration symboliques d\'efinies
et ind\'efinies sont ensuite d\'evelopp\'es, dont la justification
th\'eorique fait appel \`a la th\'eorie des~{\mathcal D}-modules holonomes.
Les premiers ont recours \`a une \'elimination polynomiale non
commutative par bases de Gr\"obner~; les seconds \`a des algorithmes
de r\'esolution de syst\`emes fonctionnels lin\'eaires en leurs
solutions fractions rationnelles. Bien plus que la recherche de
formes closes, l'objectif est de pouvoir continuer \`a calculer avec
la repr\'esentation implicite des objets holonomes m\^eme en l'absence
de formes explicites. Ce type de calculs permet en particulier la
preuve automatique d'identit\'es sommatoires et int\'egrales. Une
implantation de ces algorithmes dans le syst\`eme de calcul formel
{\sc Maple} a permis de donner la premi\`ere preuve automatique
d'identit\'es jusqu'\`a pr\'esent inaccessibles par le calcul formel.
\emph{(English)} This thesis shows how computer algebra makes it
possible to manipulate a large class of sequences and functions that
are solutions of linear operators, namely that of holonomic functions.
This class contains numerous special functions, in one or several
variables, as well as numerous combinatorial sequences. First, a
theoretical framework is introduced in order to give algorithms for
the closure properties of the holonomic class, to permit a zero test
in this class, and to unify differential calculations with functions
and calculations of recurrences with sequences. These methods are
based on calculations by an extension of the theory of Gr\"obner bases
in a framework of non-commutative polynomials, namely Ore polynomials.
Two kinds of algorithms for symbolic definite and indefinite summation
and integration are then developed, whose theoretical justification
appeals to the theory of holonomic~{\mathcal D}-modules. The former resort
to non-commutative polynomial elimination by Gr\"obner bases; the
latter to algorithms to solve linear functional systems for their
rational function solutions. Much more than the search for closed
forms, the aim is to be able to continue to compute with the implicit
representation of holonomic objects even when no explicit form is
available. In particular, this type of calculation makes the
automatic proof of summatory and integral identities possible. An
implementation of these algorithms for the computer algebra system
{\sc Maple} has made it possible to give the first automatic proof of
identities so far unreachable by computer algebra.}
}
@InProceedings{Chyzak-2011-UCP,
author = {Chyzak, Frédéric and Darrasse, Alexis},
title = {Using {C}amlp4 for presenting dynamic mathematics on the web: {DynaMoW}, an {OCaml} language extension for the run-time generation of mathematical contents and their presentation on the web},
OPTcrossref = {},
OPTkey = {},
booktitle = {ICFP'11 (September 19--21, 2011, Tokyo, Japan)},
pages = {259--265},
year = {2011},
editor = {Danvy, Olivier},
OPTvolume = {},
OPTnumber = {},
OPTseries = {},
OPTaddress = {},
OPTmonth = {},
OPTorganization = {},
publisher = {ACM},
note = {(An experience report.)},
OPTannote = {},
url = {http://ddmf.msr-inria.inria.fr/download/DynaMoW-ICFP11.pdf},
abstract = {We report on the design and implementation of a programming tool,
DynaMoW, to control interactive and incremental mathematical
calculations to be presented on the web. This tool is implemented
as a language extension of OCaml using Camlp4. Fragments of mathematical code
written for a computer-algebra system as well as
fragments of mathematical web documents are embedded directly and
naturally inside OCaml code. A DynaMoW-based application is made of
independent web services, whose parameter types are checked by the
OCaml extension. The approach is illustrated by two implementations
of online mathematical encyclopedias on top of DynaMoW.}
}
@inproceedings{ChyzakDavenportKoutschanSalvy2011,
Arxiv = {abs/1109.2809},
Author = {Chyzak, Fr{\'e}d{\'e}ric and Davenport, James H. and Koutschan, Christoph and Salvy, Bruno},
Booktitle = {SYNASC},
Date-Added = {2011-09-23 07:25:22 +0000},
Date-Modified = {2011-09-23 07:29:05 +0000},
Eprint = {1109.2809},
Month = sep,
Note = {5 pages. 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. September 26-29, 2011. Timisoara, Romania},
Title = {On {K}ahan's Rules for Determining Branch Cuts},
Url = {http://arxiv.org/abs/1109.2809},
Year = {2011},
Bdsk-Url-1 = {http://arxiv.org/abs/1109.2809},
abstract = {In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.}
}
@inproceedings{ChyzakKauersSalvy2009,
Arxiv = {abs/0904.2761},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Chyzak, Fr{\'e}d{\'e}ric and Kauers, Manuel and Salvy, Bruno},
Booktitle = {ISSAC '09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation},
Date-Added = {2009-04-20 09:01:31 +0200},
Date-Modified = {2009-08-03 14:27:59 +0200},
Doi = {10.1145/1576702.1576720},
Editor = {May, John},
Pages = {111--118},
Title = {A Non-Holonomic Systems Approach to Special Function Identities},
Year = {2009},
Abstract = {We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.},
}
@PhDThesis{Clement00,
author = "Julien Cl\'ement",
title = "Arbres Digitaux et Sources Dynamiques",
year = 2000,
month = sep,
school = "Universit\'e de Caen",
type = "Th\`ese de Doctorat"
}
@Article{ClFlVa01,
author = "Julien Cl\'ement and Philippe Flajolet and Brigitte Vall\'ee",
title = "Dynamical Sources in Information Theory: A General
Analysis of Trie Structures",
journal = "Algorithmica",
volume = 29,
number = "1/2",
year = 2001,
pages = "307--369",
url = {http://www.inria.fr/rrrt/rr-3645.html}
}
@InProceedings{ClFlVa98,
author = {Julien Cl\'ement and Philippe Flajolet and Brigitte Vall\'ee},
title = {The Analysis of Hybrid Trie Structures},
pages = {531--539},
year = 1998,
booktitle = "Proceedings of the Ninth Annual ACM--SIAM Symposium on
Discrete Algorithms",
publisher = "SIAM Press",
address = "Philadelphia",
url = {http://www.inria.fr/rrrt/rr-3295.html}
}
@article{CloteKranakisKrizancSalvy2009,
Arxiv = {abs/0908.4003},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Clote, Peter and Kranakis, Evangelos and Krizanc, Danny and Salvy, Bruno},
Date-Added = {2009-08-28 08:27:50 +0200},
Date-Modified = {2009-10-05 08:41:44 +0200},
Doi = {10.1142/S0219720009004333},
Journal = {Journal of Bioinformatics and Computational Biology},
Month = oct,
Number = {5},
Pages = {869--893},
Title = {Asymptotics of Canonical and Saturated RNA Secondary Structures},
Url = {http://www.worldscinet.com/jbcb/07/0705/S0219720009004333.html},
Volume = {7},
Year = {2009},
Abstract = {It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2}\cdot 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures --- canonical and saturated structures. Canonical secondary structures are defined to have no lonely (isolated) base pairs. This class of secondary structures was introduced by Bompf{\"u}newerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up, by proving that the asymptotic number of canonical RNA secondary structures is $2.1614 \cdot n^{-3/2} \cdot 1.96798^n$ and that the expected number of base pairs in a canonical secondary structure is $0.31724 \cdot n$. The asymptotic number of canonical secondary structures was obtained much earlier by Hofacker, Schuster and Stadler using a different method.
Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we show that the asymptotic number of saturated structures is $1.07427 \cdot n^{-3/2}\cdot 2.35467^n$, the asymptotic expected number of base pairs is $0.337361\cdot n$, and the asymptotic number of saturated stem-loop structures is $0.323954 \cdot 1.69562^n$, in contrast to the number $2^{n - 2}$ of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we apply the work of Drmota to show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs is $0.340633 \cdot n$.
}
}
@Article{CoFlFlHo98,
author = "Ed Coffman and Philippe Flajolet and Leopold Flatto and
Micha Hofri",
title = " The Maximum of a Random Walk and Its Application
to Rectangle Packing",
volume = 12,
month = jul,
year = 1998,
journal = "Probability in Engineering and Informational Sciences",
pages = "373--386",
keywords = "random walk, maximum, Rice integrals",
url = {http://www.inria.fr/rrrt/rr-3223.html}
}
@Article{CoGiGrLeRoSt95,
author = "Coffman, E.~G. and Gilbert, E.~N. and Greenberg, A.~G.
and Leighton, F.~T. and Robert, P. and Stolyar, A.~L.",
title = "Queues served by a rotating ring",
key = "Queueing Systems",
journal = "Stochastic Models",
year = 1995,
volume = 11,
number = 3,
pages = "371--394"
}
@Article{CoRoSt99,
author = {Coffman, E. G., Jr. and Robert, Ph. and Stolyar, A. J.},
title = {The Interval Packing Process of Linear Networks},
journal = "ACM SIGMETRICS Performance Evaluation Review",
year = 1999,
volume = 27,
number = 3,
month = dec,
pages = {3-4},
}
@TechReport{DaDu97,
author = "Dantzer, Jean-Francois and Dumas, Vincent",
title = "Conditions d'ergodicit\'e de l'anneau de Cambridge
et de certaines de ses faces. Limites fluides",
institution = "Institut National de Recherche en Informatique et en
Automatique",
year = 1997,
type = "Research report",
number = 3320,
month = Dec,
url = {http://www.inria.fr/rrrt/rr-3320.html}
}
@Article{DaFlVa97,
author = {Herv{\'e} Daud{\'e} and Philippe Flajolet and Brigitte
Vall{\'e}e},
title = {An Average-case Analysis of the Gaussian Algorithm for
Lattice Reduction},
journal = {Combinatorics, Probability and Computing},
year = 1997,
volume = 6,
number = 4,
month = dec,
pages = {329--349},
url = {http://www.inria.fr/rrrt/rr-2798.html}
}
@Article{DaHaRo00,
author = {Dantzer, Jean-Fran\c{c}ois and Haddani, Mostapha and Robert, Philippe},
title = {On the stability of a bandwidth packing algorithm},
journal = "Probability in the Engineering and Informational Sciences",
year = 2000,
volume = 14,
number = 1,
pages = {57--79}
}
@Article{DaMiRo01,
author = {Jean-Fran\c{c}ois Dantzer and Isi Mitrani and Philippe Robert},
title = {Large Scale and Heavy Traffic Asymptotics for Systems with Unreliable Servers},
journal = "Queueing Systems, Theory and Applications",
year = {2001},
volume = 38,
number = 1,
pages = {5--24},
url = {http://www.inria.fr/rrrt/rr-3807.html}
}
@PhdThesis{Dantzer00,
author = {Jean-Fran{\c{c}}ois Dantzer},
title = {Stabilit{\'e} des r{\'e}seaux de files d'attente et limites fluides stochastiques},
school = {Universit{\'e} de Versailles-St Quentin},
year = 2000,
type = {Th{\`e}se de Doctorat},
}
@TechReport{DaRo00,
author = {Dantzer, Jean-Fran\c{c}ois and Robert, Philippe},
title = {Analysis of a multi-class queueing system},
institution = {INRIA},
type = {Rapport de Recherche},
number = 4037,
year = 2000,
url = {http://www.inria.fr/rrrt/rr-4037.html},
month = oct
}
@Article{DeFlHuNoSt99,
author = "Luc Devroye and Philippe Flajolet and Ferran Hurtado
and Marc Noy and William Steiger",
title = "Random Triangulations",
year = 1999,
journal = "Discrete and Computational Geometry",
pages = "105--117",
keywords = "triangulation, Catalan domain"
}
@InProceedings{DeReVa01,
author = {A. Denise and M. R{\'e}gnier and M. Vandenbogaert},
title = {Assessing statistical significance of overrepresented oligonucleotides},
booktitle = {WABI'01},
year = {2001},
pages = {85--97},
publisher = {Springer-Verlag},
editors ={O. Gascuel and B. Moret},
note = {Proc. First Intern. Workshop on Algorithms in Bioinformatics, Aarhus, Denmark, August 2001},
url = {http://algo.inria.fr/regnier/publis/DeReVa01.ps}
}
@Book{DrFlGaGi04,
title = {Mathematics and Computer Science III: Algorithms,
Trees, Combinatorics and Probabilities},
series ="Trends in Mathematics (Mathematics, Computer Science)",
editor = "Drmota, M. and Flajolet, P. and Gardy, D. and Gittenberger, B.",
year = 2004,
note = "554 pages.",
publisher ="{Birkh{\"a}user Verlag}",
}
@Article{DrSo95,
author = "Michael Drmota and Mich\`ele Soria",
title = "Marking in Combinatorial Constructions:
Generating Functions and Limiting Distributions",
year = 1995,
volume = 144,
number = "1--2",
journal = "Theoretical Computer Science",
pages = "67--99",
}
@article{DrSo97,
Author = {Drmota, Michael and Soria, Mich{\`e}le},
Journal = {SIAM Journal on Discrete Mathematics},
Month = may,
Number = 2,
Pages = {246--269},
Title = {Images and Preimages in Random Mappings},
Volume = 10,
Year = 1997}
@InProceedings{DuFl03,
title = "Loglog Counting of Large Cardinalities",
author = "Marianne Durand and Philippe Flajolet",
year = 2003,
month = sep,
booktitle = "Annual European Symposium on Algorithms (ESA03)",
series = "Lecture Notes in Computer Science",
volume = "2832",
pages = "605--617",
editor = "Di Battista, G. and Zwick, U.",
}
@Article{DuFl96,
author = {Dumas, Ph. and Flajolet, Ph.},
title = {Asymptotique des r\'ecurrences mahleriennes: le cas
cyclotomique},
journal = {Journal de
th{\'e}orie des nombres de Bordeaux},
year = 1996,
volume = 8,
url = {http://algo.inria.fr/papers/other/DuFl96.ps.gz}
}
@article{DuFlLoSc04,
author = "Philippe Duchon and Philippe Flajolet and Guy Louchard and
Gilles Schaeffer",
title = "Boltzmann Samplers for the Random Generation
of Combinatorial Structures",
year = 2004,
journal = "Combinatorics, Probability and Computing",
volume = 13,
number = "4--5",
pages = "577--625",
note = "Special issue on Analysis of Algorithms.",
}
/pre>
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Bruno Salvy at 2008-08-07 14:08:54 +0200
%% Saved with string encoding Unicode (UTF-8)
@inproceedings{DuFoSa08,
Arxiv = {abs/0803.1975},
Author = {Dumas, Jean-Guillaume and Fousse, Laurent and Salvy, Bruno},
Booktitle = {Milestones in Computer Algebra (MICA 2008)},
Date-Added = {2008-04-01 13:50:07 +0200},
Date-Modified = {2008-08-07 14:08:49 +0200},
Editor = {Moreno Maza, Marc and Watt, Stephen M.},
Month = may,
Note = {Proceedings of a conference in honour of Keith Geddes' 60th birthday. Stonehaven Bay, Trinidad and Tobago, 1-3 May 2008},
Title = {Compressed Modular Matrix Multiplication},
Url = {http://algo.inria.fr/papers/pdf/DumasFousseSalvy2008.pdf},
Year = {2008},
Abstract = {Matrices of integers modulo a small prime can be compressed by storing several entries into a single machine word.
Modular addition is performed by addition and possibly subtraction of a word containing several times
the modulo. We show how modular multiplication can also be performed. In terms of arithmetic operations, the gain over
classical matrix multiplication is equal to the number of integers
that are stored inside a machine word. The gain in actual speed is also close to that number.
First, modular dot product can be performed via an integer multiplication by
the reverse integer.
Modular multiplication by a word containing a
single residue is also possible.
We give bounds on the
sizes of primes and matrices for which such a compression is
possible. We also make explicit the details of the required
compressed arithmetic routines and show some practical
performance.
}}
@TechReport{DuGo95,
author = "Philippe Dumas and Xavier Gourdon",
title = "Une introduction {\`a} Maple",
institution = "Institut National de Recherche en Informatique et en
Automatique",
year = 1995,
type = "Technical Report",
number = 173,
url = {http://www.inria.fr/rrrt/rt-0173.html}
}
@Book{DuGo97,
author = {Philippe Dumas and Xavier Gourdon},
title = {Maple Son bon usage en math\'ematiques},
publisher = {Springer-Verlag},
year = 1997,
note = {ISBN 3-540-63140-2}
}
@InProceedings{DuGuRo01a,
author = {Alain Dupuis and Fabrice Guillemin and Philippe Robert},
title = {Modeling Max-Min Fairness for Elastic Flows in Telecommunication Networks},
booktitle = {ITC'17},
year = 2001,
address = {Salvador da Bahia},
month = dec,
}
@InProceedings{DuGuRo01,
author = {Vincent Dumas and Fabrice Guillemin and Philippe Robert},
title = {Limit results for {M}arkovian models of TCP},
booktitle = {Globecom'2001},
year = 2001,
address = {San Antonio},
month = nov,
}
@InProceedings{DuLiWa04,
author = {Lipmaa, Helger and Wall{\'e}n, Johan and Dumas, Philippe},
title = {Differential Probability of Exclusive-Or},
booktitle = {Fast Software Encryption 2004},
pages = {317--331},
year = 2004,
editor = {Roy, Bimal and Meier, Willi},
volume = {3017},
series = {Lecture Notes in Computer Science},
publisher = {Springer-Verlag},
note = {Delhi, India, February 5--7, 2004},
}
@article{DuLiWa07,
author = {Dumas, Philippe and Lipmaa, Helger and Wall{\'e}n, Johan},
title = {Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation},
journal = {Discrete Mathematics \& Theoretical Computer Science},
volume = {9},
number = {1},
year = {2007},
pages = {247--274},
issn = {1365-8050},
url = {http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/478/1836}
}
@TechReport{Dumas08,
arXiv = {0807.1523},
author = {Dumas, Philippe},
title = {Mean asymptotic behaviour of radix-rational
sequences and dilation equations (Extended version)},
institution = {arXiv},
year = 2008,
abstract = {The generating series of a radix-rational sequence
is a rational formal power series from formal
language theory viewed through a fixed radix
numeration system. For each radix-rational sequence
with complex values we provide an asymptotic
expansion for the sequence of its Ces\`aro
means. The precision of the asymptotic expansion
depends on the joint spectral radius of the linear
representation of the sequence; the coefficients are
obtained through some dilation equations. The proofs
are based on elementary linear algebra.},
url = {http://arxiv.org/abs/0807.1523},
date-added = {2008-07-09 19:15:48 GMT},
date-modified ={2008-08-21 19:52:55 GMT}}
@string{LNCS = "Lecture Notes in Computer Science"}
@InProceedings{Dumas93a,
author = {Dumas, Ph.},
title = {Algebraic Aspects of {B}-regular Series},
booktitle = {Automata, Languages and Programming},
year = 1993,
editor = {A. Lingas and R. Karlsson and S. Carlsson},
pages = {457--468},
organization = {EATCS},
publisher = {Springer Verlag},
series = LNCS,
note = {Proceedings of the 20th International Colloquium
ICALP 93, Lund, Sweden} ,
url = {http://algo.inria.fr/papers/other/Dumas93a.ps.gz}
}
@PhDThesis{Dumas93,
author = {Ph. Dumas},
title = {R{\'e}currences Mahl{\'e}riennes, suites automatiques et
\'etudes asymptotiques},
type = {Doctorat de Math\'ematiques},
school = {Universit\'e de Bordeaux~I},
year = 1993,
Url = {ftp://ftp.inria.fr/INRIA/publication/Theses/TU-0252/}
}
@article{DumasFousseSalvy2011,
Author = {Dumas, Jean-Guillaume and Fousse, Laurent and Salvy, Bruno},
Date-Added = {2010-11-30 08:43:20 +0100},
Date-Modified = {2011-05-19 07:05:57 -0700},
Doi = {10.1016/j.jsc.2010.08.015},
Issn = {0747-7171},
Journal = {Journal of Symbolic Computation},
Keywords = {Compressed matrix multiplication},
Month = jul,
Number = {7},
Askreprint = {Bruno.Salvy@inria.fr},
Pages = {823--840},
Title = {Simultaneous modular reduction and {K}ronecker substitution for small finite fields},
Volume = {46},
Year = {2011},
Abstract = {
We present algorithms to perform modular polynomial multiplication or a modular dot product efficiently in a single machine word. We use a combination of techniques. Polynomials are packed into integers by Kronecker substitution; several modular operations are performed at once with machine integer or floating point arithmetic; normalization of modular images is avoided when possible; some conversions back to polynomial coefficients are avoided; the coefficients are recovered efficiently by preparing them before conversion. We discuss precisely the required control on sizes and degrees. We then present applications to polynomial multiplication, prime field linear algebra and small extension field arithmetic, where these techniques lead to practical gains of quite large constant factors.}
}
@Article{Durand03,
author = {Marianne Durand},
title = {Asymptotic Analysis of an Optimized Quicksort Algorithm},
year = "2003",
volume = 85,
pages = {73--77},
journal = " Information Processing Letters"
}
@PhdThesis{Durand04,
author = "Marianne Durand",
title = "Combinatoire analytique et algorithmique des ensembles de donn{\'e}es",
school = "{\'E}cole polytechnique",
year = "2004",
url = {http://algo.inria.fr/papers/pdf/Durand04.pdf},
type = "Th{\`e}se de Doctorat"
}
@Article{DuRo01,
author = {Vincent Dumas and Philippe Robert},
title = {On the maximum throughput of a resource sharing model},
journal = "Mathematics of Operation Research",
volume = {26},
number = {1},
year = {2001},
pages = "163--173",
}
@Article{DuTa03,
author = "Marianne Durand and Stephen Taylor",
title = "Emerging Behavior as Binary Search Trees Are Symetrically Updated",
journal = "Theoretical Computer Science",
volume = "297",
year = "2003",
pages = "425--445",
keywords = "asymptotics, generating functions"
}
@Article{DuTh95,
author = {Dumas, Ph. and Thimonier, L.},
title = {Random palindromes: multivariate generating function
and {B}ernoulli density},
journal = {Discrete Mathematics},
year = 1995,
volume = 139,
number = {1--3},
pages = {143--154},
url = {http://www.inria.fr/papers/other/DuTh95.ps.gz}
}
@Inproceedings{FaWa05,
author={Julien Fayolle and Mark Daniel Ward},
title={Analysis of the Average Depth in a Suffix Tree under a Markov Model},
editor = {Conrado Mart{\'\i}nez},
booktitle = {2005 International Conference on Analysis of Algorithms},
series = {DMTCS Proceedings},
publisher = {Discrete Mathematics and Theoretical Computer Science},
year = 2005,
volume = {AD},
pages = {95--104},
url = {http://www.dmtcs.org/proceedings/html/dmAD0109.abs.html}
}
@Misc{Fayolle02,
author = "Fayolle, Julien",
title = "Param\`etres des arbres suffixes dans le cas de sources simples",
year = 2002,
note = "M\'emoire de DEA, Universit\'e Paris VI."
}
@InProceedings{Fayolle04,
author="Julien Fayolle",
title="An average-case analysis of basic parameters of the suffix tree",
pages="217--227",
booktitle= "Mathematics and Computer Science",
editor = "Michael Drmota and Philippe Flajolet and Dani{\`e}le Gardy and Bernhard Gittenberger",
year = "2004",
publisher = "Birkh{\"a}user",
note = "Proceedings of a colloquium organized by TU Wien,
Vienna, Austria, September 2004"
}
@phdthesis{Fayolle06,
Author = {Julien Fayolle},
Date-Added = {2006-08-30 20:22:52 +0200},
Date-Modified = {2006-08-30 20:30:57 +0200},
School = {\'Ecole doctorale en informatique, t\'el\'ecommunication et \'electronique de l'Universit\'e Pierre et Marie Curie},
Title = {Compression de donn\'ees sans perte et combinatoire analytique},
type = {Th{\`e}se de Doctorat},
url = {http://algo.inria.fr/papers/pdf/Fayolle06.pdf},
Year = {2006}}
@Article{FiFlKa05,
title = "Singularity Analysis, {H}adamard Products, and Tree Recurrences",
author = "James A. Fill and Philippe Flajolet and Nevin Kapur",
journal = "Journal of Computational and Applied Mathematics",
year = 2005,
month = feb,
volume = 174,
pages = "271--313"
}
@Article{Flajolet01,
author = "Philippe Flajolet",
title = "{$D\cdot E\cdot K =(100)_8$}",
journal = "Random Structures \& Algorithms",
year = 2001,
volume = 19,
number = "3/4",
pages = "150--162",
note = "Introduction to special volume on ``Analysis of Algorithms''
dedicated to D. E. Knuth."
}
@InProceedings{Flajolet02,
author = "Philippe Flajolet",
title = "Singular Combinatorics",
year = 2002,
publisher = "World Scientific",
booktitle = "Proceedings of the International Congress of Mathematicians",
editor = "Li Tatsien",
pages = "561--571",
volume = "{III}",
note = "Invited lecture, ICM02, Beijing, China, 20--28 August 2002."
}
@InProceedings{Flajolet04,
author = "Philippe Flajolet",
title = "Counting by coin tossings",
booktitle = "{Proceedings of ASIAN'04 (Ninth Asian Computing
Science Conference)}",
series = "Lecture Notes in Computer Science",
volume = "3321",
editor = "Maher, M.",
pages = "1--12",
year = 2004,
note = "Text of Opening Keynote Address."
}
@article{FlDuPu06,
Author = {Flajolet, Philippe and Dumas, Philippe and Puyhaubert, Vincent},
Journal = {Discrete Mathematics \& Theoretical Computer Science (Proceedings)},
Pages = {59--118},
Title = {Some exactly solvable models of urn process theory},
Volume = {AG},
Year = {2006}}
@article{FlSzVa06,
Author = {Flajolet, Philippe and Szpankowski, Wojciech and Vall\'ee, Brigitte},
Journal = {Journal of the ACM},
Month = jan,
Number = {1},
Pages = {147--183},
Title = {Hidden Word Statistics},
Volume = {53},
Year = 2006}
@inproceedings{Flajolet06,
Author = {Flajolet, Philippe},
Booktitle = {{STACS~2006}},
Editor = {Durand, Bruno and Thomas, Wolfgang},
Note = {Proceedings of 23rd Annual Symposium on Theoretical Aspects of Computer Science, Marseille, February 2006.},
Pages = {1--22},
Series = {Lecture Notes in Computer Science},
Title = {The Ubiquitous Digital Tree},
Volume = 3884,
Year = 2006}
@article{CoFl06,
Author = {Conrad, Eric van Fossen and Flajolet, Philippe},
Journal = {S\'eminaire Lotharingien de Combinatoire},
Number = {B54g},
Pages = {1--44},
Title = {The {Fermat} cubic, elliptic functions, continued fractions, and a combinatorial excursion},
Volume = 54,
Year = 2006}
@article{FlNePr06,
Author = {Flajolet, Philippe and Nebel, Markus and Prodinger, Helmut},
Journal = {Theoretical Computer Science},
Month = apr,
Number = 3,
Pages = {371--381},
Title = {The scientific works of {Rainer Kemp} (1949--2004)},
Volume = 355,
Year = 2006}
@Incollection{Flajolet97b,
author = "Philippe Flajolet",
title = "Adaptive Sampling",
booktitle = "Encyclopaedia of Mathematics",
publisher = "Kluwer Academic Publishers",
address = "Dordrecht",
year = 1997,
pages = 28,
volume = "Supplement~{I}",
editor = "M. Hazewinkel"
}
@Article{Flajolet99,
author = "Philippe Flajolet",
title = "Singularity analysis and asymptotics of {Bernoulli} sums",
journal = "Theoretical Computer Science",
year = 1999,
volume = 215,
number = "1-2",
pages = "371--381",
keywords = "singularity analysis, information theory, polylogarithm",
url = {http://www.inria.fr/rrrt/rr-3401.html}
}
@article{FlajoletGerholdSalvy2010,
Arxiv = {abs/0906.1957},
Author = {Flajolet, Philippe and Gerhold, Stefan and Salvy, Bruno},
Date-Added = {2009-06-11 07:06:46 +0200},
Date-Modified = {2010-01-06 08:15:22 +0100},
Journal = {The Electronic Journal of Combinatorics},
Number = {1},
Pages = {1--28},
Title = {Lindel{\"o}f Representations and (Non-)Holonomic Sequences},
Url = {http://www.combinatorics.org/Volume_17/PDF/v17i1r3.pdf},
Volume = {17},
Year = {2010},
Abstract = {Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindel{\"o}f, which belong to an attractive but largely forgotten chapter of complex analysis. One of the outcomes of such analyses concerns the non-existence of linear recurrences with polynomial coefficients annihilating these sequences, and, accordingly, the non-existence of linear differential equations with polynomial coefficients annihilating their generating functions. In particular, the corresponding generating functions are transcendental. Asymptotics of certain finite difference sequences come out as a byproduct of our approach.}
}
%% Created for Bruno Salvy at 2008-04-24 11:37:26 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{FlFuGoPaPo06,
Arxiv = {abs/math/0606370},
Author = {Flajolet, Philippe and Fusy, {\'E}ric and Gourdon, Xavier and Panario, Daniel and Pouyanne, Nicolas},
Date-Added = {2006-12-11 18:20:46 +0100},
Date-Modified = {2008-04-24 11:37:26 +0200},
Journal = {The Electronic Journal of Combinatorics},
Month = {June},
Note = {35 pages},
Number = {1},
Pages = {R103},
Title = {A Hybrid of {D}arboux's Method and Singularity Analysis in Combinatorial Asymptotics},
Url = {http://www.combinatorics.org/Volume_13/PDF/v13i1r103.pdf},
Volume = {13},
Year = {2006},
Bdsk-Url-1 = {http://www.combinatorics.org/Volume_13/PDF/v13i1r103.pdf}}
%% Created for Bruno Salvy at 2008-04-24 11:37:42 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{FlGaPe05,
Arxiv = {abs/math/0407098},
Author = {Flajolet, Philippe and {Gabarr\'o}, Joaquim and Pekari, Helmut},
Date-Modified = {2008-04-24 11:37:42 +0200},
Journal = {Annals of Probability},
Number = 3,
Pages = {1200--1233},
Title = {Analytic Urns},
Volume = 33,
Year = 2005}
@Article{FlGoDu95,
author = "Flajolet, P. and Gourdon, X. and Dumas, P.",
title = "Mellin Transforms and Asymptotics : Harmonic Sums",
journal = "Theoretical Computer Science",
year = 1995,
volume = 144,
number = "1--2",
pages = "3--58",
url = {http://www-rocq.inria.fr/algo/flajolet/Publications/mellin-harm.ps.gz}
}
@Article{FlGoMa97,
author = {Philippe Flajolet, Xavier Gourdon and Conrado
Mart{\'\i}nez},
title = {Patterns in random binary search trees},
journal = {Random Structures and Algorithms},
year = 1997,
volume = 11,
number = 3,
month = oct,
pages = {223--244},
url = {http://www.inria.fr/rrrt/rr-2883.html}
}
@Article{FlGoPa01,
author = "Philippe Flajolet and Xavier Gourdon and Daniel Panario",
title = "The Complete Analysis of a Polynomial Factorization
Algorithm over Finite Fields",
journal = "Journal of Algorithms",
volume = 40,
number = 1,
year = 2001,
pages = "37--81",
url = {http://www.inria.fr/rrrt/rr-3370.html}
}
@InProceedings{FlGoPa96,
author = {Philippe Flajolet and Xavier Gourdon and Daniel Panario},
title = {Random Polynomials and Polynomial Factorization},
booktitle = {ICALP},
pages = {232--243},
year = 1996,
editor = {F. Meyer auf der Heide},
number = 1099,
series = {Lecture Notes in Computer Science},
publisher = {Springer-Verlag},
note = {Proceedings 23rd ICALP conference},
url = {http://www.inria.fr/rrrt/rr-2852.html}
}
@Article{FlGrKiPr95,
author = "Philippe Flajolet and Peter Grabner and Peter Kirschenhofer
and Helmut Prodinger",
title = "On {R}amanujan's {$Q$}-function",
year = "1995",
journal = "Journal of Computational and Applied Mathematics",
volume = 58,
number = 1,
pages = "103--116",
keywords = "Ramanujan, Knuth, Q(n) function, linear probing
hashing, asymptotic bounds",
url = {http://www-rocq.inria.fr/algo/flajolet/Publications/rama.ps.gz}
}
@Article{FlGrKiPrTi94,
author = "Philippe Flajolet and Peter Grabner and Peter Kirschenhofer
and Helmut Prodinger and Robert Tichy",
title = "{M}ellin Transforms and Asymptotics: Digital Sums",
year = 1994,
journal = "Theoretical Computer Science",
volume = 123,
pages = "291--314",
number = 2,
keywords = "Mellin transforms, digital sum, number representation",
url = {http://www-rocq.inria.fr/algo/flajolet/Publications/mellin-dig.ps.gz}
}
@Article{FlGu00,
author = "Philippe Flajolet and Fabrice Guillemin",
title = "The Formal Theory of Birth-and-Death Processes, Lattice
Path Combinatorics, and Continued Fractions",
journal = "Advances in Applied Probability",
volume = 32,
year = 2000,
pages = "750--778",
url = {http://www.inria.fr/rrrt/rr-3667.html}
}
@InProceedings{FlGuSzVa01,
author = "Philippe Flajolet and Yves Guivarc'h and Wojtek Szpankowski and
Brigitte Vall\'ee",
title = "Hidden Pattern Statistics",
year = 2001,
series = "Lecture Notes in Computer Science",
publisher = "Springer Verlag",
number = 2076,
booktitle = "Automata, Languages, and Programming",
editor = "F. Orejas and P. Spirakis and J. van Leeuwen",
pages = "152--165",
note = "Proceedings of the 28th ICALP Conference, Crete,
July 2001."
}
@InProceedings{FlHaNiSp00,
author = "Philippe Flajolet and Kostas Hatzis and
Sotiris Nikoletseas and Paul Spirakis",
title = "Trade-offs between density and robustness
in random interconnection graphs",
booktitle = "IFIP International Conference on Theoretical Computer Science",
year = 2000,
month = aug,
series = "Lecture Notes in Computer Science",
volume = 1872,
pages = "152--168",
editor = "J van Leeuwen and O. Watanabe and M. Hagiya and
P.~D. Moses and T. Ito",
note = "(Proceedings of IFIP TCS'2000, Sendai, August 2000.)"
}
@Article{FlHaNiSp02,
author = "Philippe Flajolet and Kostas Hatzis and
Sotiris Nikoletseas and Paul Spirakis",
title = "On the Robustness of Interconnections in Random Graphs:
A Symbolic Approach",
journal = "Theoretical Computer Science",
year = 2002,
volume = 287,
number = 2,
pages = "513--534"
}
@incollection {FlHu08,
AUTHOR = {Flajolet, Philippe and Huillet, Thierry},
TITLE = {Analytic combinatorics of the {M}abinogion urn},
BOOKTITLE = {Fifth {C}olloquium on {M}athematics and {C}omputer {S}cience},
SERIES = {Discrete Math. Theor. Comput. Sci. Proc., AI},
PAGES = {549--571},
PUBLISHER = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
YEAR = {2008},
}@Article{FlLo01,
author = "Philippe Flajolet and Guy Louchard",
title = "Analytic Variations on the {A}iry Distribution",
year = 2001,
journal = "Algorithmica",
volume = 31,
number = 3,
pages = "361--377",
url = {http://algo.inria.fr/flajolet/Publications/Airy7.ps.gz}
}
@InProceedings{FlNo00,
author = "Philippe Flajolet and Marc Noy",
title = "Analytic Combinatorics of Chord Diagrams",
year = 2000,
booktitle = "Formal Power Series and Algebraic Combinatorics",
pages = "191--201",
editor = "D. Krob and A. A. Mikhalev and A. V. Mikhalev",
note = "(Proceedings of the 12th International Conference, FPSAC'2000;
June 2000, Moscow. {\em Lecture Notes in Computer Science})",
url = {http://algo.inria.fr/flajolet/Publications/RR3914.ps.gz}
}
@Article{FlNo99,
author = "Philippe Flajolet and Marc Noy",
title = "Analytic Combinatorics of Non-crossing Configurations",
journal = "Discrete Mathematics",
volume = 204,
number = "1-3",
year = 1999,
pages = "203--229",
note = "(Selected papers in honor of Henry W. Gould)",
url = {http://www.inria.fr/rrrt/rr-3196.html}
}
@inproceedings{FlajoletPelletierSoria2011,
Author = {Flajolet, Philippe and Pelletier, Maryse and Soria, Mich{\`e}le},
Booktitle = {ACM-SIAM Symposium on Discrete Algorithms},
Date-Added = {2011-06-15 11:30:40 +0200},
Date-Modified = {2011-11-29 16:57:56 +0000},
Editor = {Randall, Dana},
Note = {Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2011, San Francisco.},
Pages = {172--183},
Title = {On {B}uffon Machines and Numbers},
Year = {2011},
url = {http://www.siam.org/proceedings/soda/2011/SODA11_015_flajoletp.pdf}
}
@Article{FlPoVi98,
author = "Philippe Flajolet and Patricio Poblete and Alfredo Viola",
title = "On the Analysis of Linear Probing Hashing",
journal = "Algorithmica",
year = 1998,
volume = 22,
number = 4,
month = dec,
pages = "490--515",
keywords = "hashing, linear probing, Airy distribution",
url = {http://www.inria.fr/rrrt/rr-3265.html}
}
@Article{FlPr99,
author = "Philippe Flajolet and Helmut Prodinger",
title = "On {S}tirling Numbers for Complex Argument and {Hankel} Contours",
year = 1999,
journal = "SIAM Journal on Discrete Mathematics",
volume = 12,
number = 2,
pages = "155--159",
url = {http://www.inria.fr/rrrt/rr-3373.html}
}
@inproceedings {FlRoVa10,
AUTHOR = {Flajolet, Philippe and Roux, Mathieu and Vall\'ee, Brigitte},
TITLE = {Digital {T}rees and {M}emoryless {S}ources: from {A}rithmetics to {A}nalysis},
BOOKTITLE = {DMTCS Proceedings of the 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
YEAR = {2010},
PAGES = {233--260},
ISSN = {1365--8050},
URL = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAM0117/3289},
}
@TechReport{FlSe01,
author = "Philippe Flajolet and Robert Sedgewick",
title = "Analytic Combinatorics: Functional Equations, Rational and
Algebraic Functions",
number = "4103",
type = "Research Report",
institution = "INRIA",
year = 2001,
note = "98 pages."
}
@TechReport{FlSe02,
author = "Philippe Flajolet and Robert Sedgewick",
title = "Analytic Combinatorics---Symbolic Combinatorics",
number = "4103",
type = "Research Report",
institution = "INRIA",
volume = "TR-02-123",
year = 2002,
note = "186+vii pages."
}
@TechReport{FlSe03,
author = "Flajolet, Philippe and Sedgewick, Robert",
title = "Analytic Combinatorics: Basic Complex Asymptotics",
institution = {ALCOM Project},
number = "ALCOM-FT-TR-300",
year =2003,
month = nov,
type = "Research Report",
note = "133 pages. Chapters 4 and 5 of the book project
\emph{Analytic Combinatorics}"
}
@book {FlSe09,
AUTHOR = {Flajolet, Philippe and Sedgewick, Robert},
TITLE = {Analytic combinatorics},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {2009},
PAGES = {xiv+810},
ISBN = {978-0-521-89806-5},
}@Article{FlSe95,
author = "Philippe Flajolet and Robert Sedgewick",
title = "Mellin Transforms and Asymptotics : Finite Differences
and {R}ice's Integrals",
journal = "Theoretical Computer Science",
year = 1994,
volume = 144,
number = "1-2",
pages = "101--124",
url = {http://www-rocq.inria.fr/algo/flajolet/Publications/mellin-rice.ps.gz}
}
@string{INRIA = "Institut National de Recherche en Informatique et en
Automatique"}
@TechReport{FlSe96,
author = "Philippe Flajolet and Robert Sedgewick",
title = "The Average Case Analysis of Algorithms: Mellin Transform
Asymptotics",
type = "Research Report",
institution = inria,
year = 1996,
note = " pages."
}
@string{INRIA = "Institut National de Recherche en Informatique et en
Automatique"}
@TechReport{FlSe97,
author = "Philippe Flajolet and Robert Sedgewick",
title = "The Average Case Analysis of Algorithms: Multivariate
Asymptotics and Limit Distributions ",
type = "Research Report",
institution = inria,
year = 1997,
number = 3162,
month = may,
note = " 123 pages."
}
@Article{FlSo90,
author = "Philippe Flajolet and Mich{\`e}le Soria",
title = "Gaussian Limiting Distributions for the Number of
Components in Combinatorial Structures",
journal = "Journal of Combinatorial Theory, {\rm {S}eries {A}}",
year = 1990,
volume = 53,
pages = "165--182"
}
@Article{FlSo91,
author = "P. Flajolet and M. Soria",
title = "The Cycle Construction",
journal = "SIAM Journal on Discrete Mathematics",
volume = "4",
number = "1",
year = "1991",
month = feb,
pages = "58--60"
}
@Article{FlSo93,
author = "Philippe Flajolet and Mich{\`e}le Soria",
title = "General Combinatorial Schemas: {G}aussian limit distributions
and exponential tails",
journal = "Discrete Mathematics",
year = 1993,
volume = 114,
pages = "159--180",
}
@InProceedings{FlSz00,
author = "Philippe Flajolet and Wojtek Szpankowski",
title = "Analytic Variations on the Redundancy Rate of Renewal Processes",
booktitle = "{2000 IEEE International Symposium on Information Theory}",
publisher = "IEEE Information Theory Society",
year = 2000,
pages = "499",
note = "Short abstract",
url = {http://www.inria.fr/rrrt/rr-3553.html}
}
@Article{FlSz02,
author = "Philippe Flajolet and Wojtek Szpankowski",
title = "Analytic Variations on Redundancy Rates of Renewal Processes",
number = 11,
volume = 48,
journal = "IEEE Transactions on Information Theory",
year = 2002,
pages = "2911--2921"
}
@InProceedings{FlVa00,
author = "Philippe Flajolet and Brigitte Vall{\'e}e",
title = "Continued Fractions, Comparison Algorithms, and Fine
Structure Constants",
booktitle = "{Analysis and Applications}",
series = "Conference Proceedings, Canadian Mathematical Society",
year = 2000,
editor = "M. Th{\'e}ra",
publisher = "American Mathematical Society",
address = "Providence",
pages = "53--82",
volume = 27,
url = {http://algo.inria.fr/flajolet/Publications/thera10.ps.gz}
}
@Article{FlVa98,
author = "Philippe Flajolet and Brigitte Vall\'ee",
title = "Continued Fraction Algorithms, Functional
Operators, and Structure Constants",
journal = "Theoretical Computer Science",
year = 1998,
volume = 194,
number = {1--2},
month = mar,
pages = {1--34},
url = {http://www.inria.fr/rrrt/rr-2931.html}
}
@proceedings{FlZi92,
editor = "Philippe Flajolet and Zimmerman, P.",
title = "Algorithms Seminar, 1991--1992",
volume = "1779",
series = "Research Report",
organization = "Institut National de Recherche en Informatique et en
Automatique",
year = 1992,
url = {http://www.inria.fr/rrrt/rr-1779.html}
}
@Article{FlZiVa94,
author = "Philippe Flajolet and Paul Zimmerman and Van~Cutsem, Bernard ",
title = "A Calculus for the Random Generation of Labelled
Combinatorial Structures",
journal = "Theoretical Computer Science",
volume = 132,
number = "1-2",
year = 1994,
pages = "1--35",
keywords = "random generation, complexity calculus, simulation",
url = {http://www.inria.fr/rrrt/rr-1830.html}
}
@Book{FrGaSo90,
author = "Christine Froidevaux and Marie-Claude Gaudel and
Mich{\`e}le Soria",
title = "Types de donn{\'e}es et algorithmes",
publisher = "Ediscience",
year = "1990",
address = "Paris"
}
@Article{FrRoTi99a,
author = {Christine Fricker and Philippe Robert and Danielle Tibi},
title = {On the rates of convergence of {E}rlang's model},
journal = "Journal of Applied Probability",
volume = 36,
number = 4,
pages = "1--18",
year = 1999,
}
@InProceedings{FrRoTi99b,
author = {Christine Fricker and Philippe Robert and Danielle Tibi},
title = {Convergence to equilibrium of finite {M}arkov chains},
booktitle = {INFORMS AP99},
year = 1999,
editor = {Volker Schmidt},
address = {Ulm},
month = {Juillet}
}
@inproceedings {Fusy05,
author = {{\'E}ric Fusy},
year = {2006},
title = {Transversal structures on triangulations, with application to straight-line drawing},
editor = {Healy, Patrick and Nikolov, Nikola S.},
pages = {177--188},
booktitle = {Graph Drawing 2005},
note = {Limerick, Ireland, September 12--14, 2005},
publisher = {Springer},
series={Lecture Notes in Computer Science},
volume = {3843},
}
@article{Fusy06b,
author = {{\'E}ric Fusy},
title = {Counting d-polytopes with (d+3) vertices},
journal = {Electronic Journal of Combinatorics},
volume = {13},
number = {1},
year = {2006},
url = {http://www.combinatorics.org/Volume_13/PDF/v13i1r23.pdf},
}
@inproceedings{BoFuPi06,
author = {Olivier Bodini and {\'E}ric Fusy and Carine Pivoteau},
title = {Random sampling of plane partitions},
booktitle = {Gascom 2006},
year = {2006},
pages = {124--135},
editor = {Renzo Pinzani and Vincent Vajnovszki},
publisher = {LE2I},
address = {Dijon, France},
}
@ Inproceedings{FusyAofa05,
author = {{\'E}ric Fusy},
title = {Quadratic exact size and linear approximate size random generation of planar graphs},
editor = {Conrado Mart{\'\i}nez},
booktitle = {2005 International Conference on Analysis of Algorithms},
series = {DMTCS Proceedings},
publisher = {Discrete Mathematics and Theoretical Computer Science},
year = 2005,
volume = {AD},
pages = {125-138},
url = {http://www.dmtcs.org/proceedings/abstracts/dmAD0112.abs.html}
}
@inproceedings{FusyPS05,
author = {{\'E}ric Fusy and
Dominique Poulalhon and
Gilles Schaeffer},
title = {Dissections and trees, with applications to optimal mesh
encoding and to random sampling},
booktitle = {SODA},
year = {2005},
pages = {690--699},
note = {Proceedings of the Sixteenth Annual ACM-SIAM Symposium on
Discrete Algorithms, SODA 2005, Vancouver, British Columbia,
Canada, January 23-25, 2005}}
@InProceedings{GeLeLi04,
author = {Keith Geddes and Ha Le and Ziming Li},
title = "{Differential rational normal forms and a
reduction algorithm for hyperexponential functions}",
booktitle = {Symbolic and Algebraic Computation},
editor = {J. Gutierrez},
pages = {183--190},
publisher = {ACM Press},
year = 2004,
note = {Proceedings of ISSAC'04, Santander, July 2004}
}
@Misc{Giroire03,
author = "Giroire, Fr\'ed\'eric",
title = "Etude de Probl\`emes Combinatoires li\'es \`a l'Analyse du
G\'enome : S\'equen\c{c}age et Polymorphisme",
year = 2003,
note = "M\'emoire de DEA, Universit\'e Paris VI."
}
@inproceedings{Giroire05,
author = {Fr{\'e}d{\'e}ric Giroire},
title = {Order statistics and estimating cardinalities of massive data sets},
editor = {Conrado Mart{\'\i}nez},
booktitle = {2005 International Conference on Analysis of Algorithms},
series = {DMTCS Proceedings},
publisher = {Discrete Mathematics and Theoretical Computer Science},
year = 2005,
volume = {AD},
pages = {157-166},
url = {http://www.dmtcs.org/proceedings/html/dmAD0115.abs.html}
}
@phdthesis{Giroire06b,
Author = {Giroire, Fr{\'e}d{\'e}ric},
Date-Added = {2006-12-11 18:37:21 +0100},
Date-Modified = {2006-12-11 18:40:15 +0100},
Month = nov,
School = {Universit\'e Paris VI},
Title = {R{\'e}seaux, algorithmique et analyse combinatoire de grands ensembles},
Url = {http://algo.inria.fr/papers/pdf/Giroire06b.pdf},
Year = {2006}}
@InProceedings{Giroire06,
author = "F. Giroire",
title = "Directions to use Probabilistic Algorithms for
Cardinality for {DNA} Analysis",
Booktitle = {Journ\'ees Ouvertes Biologie Informatique
Math\'ematiques (JOBIM 2006)},
month=jul,
year = 2006,
pages={3--5}
}
@Book{Gourdon94a,
author = "Xavier Gourdon",
title = "Les maths en t\^ete, math\'ematiques pour $M'$,
Alg\`ebre",
publisher = "Ellipse",
year = "1994",
note = "288 pages",
}
@Book{Gourdon94b,
author = "Xavier Gourdon",
title = "Les maths en t\^ete, math\'ematiques pour $M'$,
Analyse",
publisher = "Ellipse",
year = "1994",
note = "416 pages",
}
@PhdThesis{Gourdon96,
author = {Gourdon, Xavier},
title = {Combinatoire, algorithmique et g{\'e}om{\'e}trie des polyn{\^o}mes},
school = {{\'E}cole polytechnique},
year = 1996,
type = {Th{\`e}se de Doctorat},
url = {http://algo.inria.fr/papers/other/Gourdon96.ps},
}
@Article{HiRe00,
author = {Daniel Hirschberg and Mireille R{\'e}gnier},
title = "Tight {B}ounds on the {N}umber of {S}tring {S}ubsequences",
journal = "Journal of Discrete Algorithms",
year = 2000,
volume = 1,
number =1,
pages = "123--132",
note = {preliminary version at CPM'99},
}
@InBook{HuFl05,
author = "Huet, {G\'erard} and Flajolet, Philippe",
chapter = "Math\'ematiques et Informatique",
title = "Les math\'ematiques dans le monde scientifique contemporain",
pages = {215--237},
publisher = {Acad\'emie des sciences},
address = "Paris",
year = 2005,
series = "Rapport sur la science et la technologie",
volume = 20,
note = "Edited by Jean-Cristophe Yoccoz"
}
@InProceedings{JaMuRo95b,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {Using {QoS} parameters to support various traffics on {CATV}
multiple access {MAC}},
booktitle = {IEEE 802.14 Normalization Conference},
year = 1995,
pages = {172}
}
@InProceedings{JaMuRo95,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {{CATV} slotted multiple access {MAC}},
booktitle = {IEEE 802.14 Normalization Conference},
pages = {166},
year = 1995
}
@InProceedings{JaMuRo95c,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {Performant implementations of tree collision resolution on {CATV} network},
booktitle = {IEEE 802.14 Normalization Conference},
year = 1995,
pages = {115}
}
@InProceedings{JaMuRo96b,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {Simulation of a stack algorithm with priorities and reservations},
booktitle = {IEEE 802.14 Normalization Conference},
Year = 1996,
pages = {181}
}
@InProceedings{JaMuRo96,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {A unified approach for {CATV} networks capable of mixing {ATM}
and non {ATM} traffics with {CBR} and non {CBR} traffics},
booktitle = {IEEE 802.14 Normalization Conference},
year = 1996,
pages = {180}
}
@InProceedings{JaMuRo96c,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {Framing protocols on upstream channel in {CATV} networks:
asymptotic average delay analysis},
booktitle = {IEEE 802.14 Normalization Conference},
year = 1996,
pages = {247}
}
@InProceedings{JaMuRo96d,
author = {Philippe Jacquet and Paul M{\"u}hlethaler and Philippe Robert},
title = {Asymptotic average access delay analysis: adaptive p-persistence versus tree algorithm},
booktitle = {IEEE 802.14 Normalization Conference},
year = 1996,
pages = {248}
}
@InProceedings{KiFlYa00,
author = "John Kieffer and Philippe Flajolet and En-Hui Yang",
title = "Data Compression Via Binary Decision Diagrams",
booktitle = "{2000 IEEE International Symposium on Information Theory}",
publisher = "IEEE Information Theory Society",
year = 2000,
pages = "296",
note = "(Short abstract)."
}
@Article{KoMaRo00,
author = {Kotz, Samuel and Mahmoud, Hosam and Robert, Philippe},
title = {On Generalized {P}\'olya Urn Models},
journal = "Statistics \& Probability Letters",
year = 2000,
volume = 49,
number = 2,
pages = "163--173",
}
@phdthesis{Lecerf01,
Author= {Gr{\'e}goire Lecerf},
title = {Une alternative aux m{\'e}thodes de r{\'e}{\'e}criture pour la r{\'e}solution des syst{\`e}mes alg{\'e}briques},
school = {{\'E}cole polytechnique},
url = {http://algo.inria.fr/papers/pdf/Lecerf01.pdf},
type = {Th{\`e}se de Doctorat},
year = 2001}
@InProceedings{LeLi04,
author = {Ha Le and Ziming Li},
title = "{Differential rational normal forms and representations of
hyperexponential functions}",
booktitle = {Rhine Workshop on Computer Algebra},
pages = {3--12},
year = 2004,
note = {Proceedings of RWCA'04, Nijmegen, March 2004.}
}
@InProceedings{LeMo98a,
author = {R. Lercier and F. Morain},
title = {Algorithms for computing isogenies between elliptic curves},
booktitle = {Computational Perspectives on Number Theory:
Proceedings of a Conference in Honor of A. O. L. Atkin},
editor = {D. A. Buell and J. T. Teitelbaum},
volume = 7,
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year = 1998,
publisher = {American Mathematical Society, International Press},
pages = {77--96}
}
@Article{LeRe04,
author = "M. Lescot and M. R{\'e}gnier",
title = "Motif statistics on plants datasets",
journal = "Biophysics",
year = "2004",
volume ="48",
number = "1",
pages = "1--6",
editors ="M. Gelfand",
note = "Proc. Moscow Conference on Computational Molecular Biology, MCCMB'03",
url = {http://algo.inria.fr/regnier/publis/LeRe03.ps}
}
@Article{LiDu93,
author = {B. Litow and Dumas, Ph.},
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@inproceedings {Lumbroso10,
AUTHOR = {Lumbroso, J{\'e}r{\'e}mie},
TITLE = {An optimal cardinality estimation algorithm based on order statistics and its full analysis},
BOOKTITLE = {DMTCS Proceedings of the 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
YEAR = {2010},
PAGES = {489--504},
}
@Article{MaFlJaRe00,
author = "Hosam Mahmoud and Philippe Flajolet and
Philippe Jacquet and Mireille R{\'e}gnier",
title = "Analytic Variations on Bucket Selection and Sorting",
journal = "Acta Informatica",
volume = 36,
pages = {735--760},
year = 2000,
number = {9-10},
url = {http://www.inria.fr/rrrt/rr-3399.html}
}
@Article{MaRo94,
author = "Malyshev, V.A. and Robert, P.",
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number = 4,
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html = {[ps]}
}
@InProceedings{MaSe02,
author = {Matera, Guillermo and Sedoglavic, Alexandre},
title = {The differential {H}ilbert function of a differential
rational mapping can be computed in polynomial time},
booktitle = {Proceedings of the 2002 International Symposium on
Symbolic and Algebraic Computation},
pages = {184--191},
year = 2002,
editor = {Mora, Teo},
address = {Lille, France},
month = jul # {~7--10},
organization = {Association for Computing Machinery},
publisher = {ACM press}
}
@Article{MaSmRe97,
author = "Hosam M. Mahmoud and Robert T. Smythe and Mireille R{\'e}gnier",
title = "Analysis of {B}oyer-{M}oore-{H}orspool String-Matching Heuristic",
journal = "Random Structures and Algorithms",
year = 1997,
volume = 10,
number = {1-2},
pages = {169--186},
url = {http://algo.inria.fr/papers/other/stringmatch.ps.gz}
}
@inproceedings{Mezzarobba2010,
Arxiv = {abs/1002.3077},
Author = {Mezzarobba, Marc},
Booktitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010)},
Date-Added = {2010-02-17 09:52:10 +0100},
Date-Modified = {2010-09-22 10:58:13 +0200},
Doi = {10.1145/1837934.1837965},
Institution = {arXiv},
Pages = {139--145},
Publisher = {ACM},
Title = {Num{G}fun: a Package for Numerical and Analytic Computation with {D}-finite Functions},
Year = {2010},
Abstract = {This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky. In some cases, our descriptions contain small improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.}
}
@phdthesis{Mezzarobba2011,
Address = {Palaiseau, France},
Author = {Mezzarobba, Marc},
Date-Added = {2011-09-05 10:12:02 +0200},
Date-Modified = {2011-11-23 11:02:38 +0000},
Month = nov,
School = {{\'E}cole polytechnique},
Title = {Autour de l'{\'e}valuation num{\'e}rique des fonctions D-finies},
Type = {PhD thesis},
Year = {2011},
url = {http://algo.inria.fr/papers/pdf/these-mezzarobba-preliminaire.pdf},
}
@article{MezzarobbaSalvy2010,
Arxiv = {abs/0904.2452},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Mezzarobba, Marc and Salvy, Bruno},
Date-Added = {2009-04-16 11:43:28 +0200},
Date-Modified = {2010-08-03 12:46:34 +0200},
Doi = {10.1016/j.jsc.2010.06.024},
Journal = {Journal of Symbolic Computation},
Month = oct,
Pages = {1075--1096},
Title = {Effective Bounds for {P}-Recursive Sequences},
Volume = {45},
Number = {10},
Year = {2010},
Abstract = {We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq v_n$ for all $n$. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of $u_n$.
We discuss applications to the evaluation of power series with guaranteed precision.}
}
@InProceedings{Mishna01,
author = {Marni Mishna},
title = {Attribute grammars and automatic complexity analysis},
booktitle = {FPSAC'01},
editors = {H. Barcelo and V. Welker},
year = 2001,
month = may,
pages = "371--380",
url = {http://algo.inria.fr/mishna/Mishna01.ps}
}
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Bruno Salvy at 2006-06-20 14:10:55 +0200
%% Saved with string encoding Western (ASCII)
@string{aa = {Acta Arithmetica}}
@string{aaecc = {Applicable Algebra in Engineering, Communication and Computing}}
@string{aam = {Advances in Applied Mathematics}}
@string{aap = {Advances in Applied Probability}}
@string{acm = {Association for Computing Machinery}}
@string{acmcs = {ACM Computing Surveys}}
@string{adm = {Annals of Discrete Mathematics}}
@string{aeq = {Aequationes Mathematicae}}
@string{ai = {Acta Informatica}}
@string{aif = {Annales de l'Institut Fourier}}
@string{aihp = {Annales de l'Institut Henri Poincar{\'e}}}
@string{am = {Advances in Mathematics}}
@string{amc = {Applied Mathematics and Computation}}
@string{amjm = {American Journal of Mathematics}}
@string{amm = {American Mathematical Monthly}}
@string{ammm = {American Mathematical Monthly}}
@string{anap = {Annals of Applied Probability}}
@string{anm = {Annals of Mathematics}}
@string{anms = {Annals of Mathematical Statistics}}
@string{anyas = {Annals of the New York Academy of Sciences}}
@string{ap = {Annals of Probability}}
@string{asmq = {Annales des Sciences Math{\'e}matiques du Qu{\'e}bec}}
@string{aujm = {Australian Journal of Mathematics}}
@string{bit = {BIT}}
@string{blms = {Bulletin of the London Mathematical Society}}
@string{bsmf = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France}}
@string{buams = {Bulletin of the American Mathematical Society}}
@string{buro = {Cahiers du Bureau Universitaire de Recherche Op{\'e}rationnelle}}
@string{cacm = {Communications of the ACM}}
@string{cj = {Computer Journal}}
@string{cjm = {Canadian Journal of Mathematics}}
@string{cma = {Computers and Mathematics with Applications}}
@string{cmb = {Canadian Mathematical Bulletin}}
@string{comb = {Combinatorica}}
@string{cras = {Comptes-Rendus de l'Acad{\'e}mie des Sciences}}
@string{crasi = {Comptes-Rendus de l'Acad{\'e}mie des Sciences, S{\'e}rie I}}
@string{crelle = {Journal f{\"u}r die reine und angewandte Mathematik}}
@string{dam = {Discrete Applied Mathematics}}
@string{dm = {Discrete Mathematics}}
@string{dma = {Discrete Mathematics and Applications}}
@string{ejc = {European Journal of Combinatorics}}
@string{eljc = {Electronic Journal of Combinatorics}}
@string{em = {L'Enseignement Math{\'e}matique}}
@string{exm = {Expositiones Mathematicae}}
@string{expm = {Experimental Mathematics}}
@string{fm = {Fundamenta Mathematicae}}
@string{fq = {Fibonacci Quarterly}}
@string{ic = {Information and Control}}
@string{ieeeit = {IEEE Transactions on Information Theory}}
@string{ijcm = {International Journal of Computer Mathematics}}
@string{ijm = {Illinois Journal of Mathematics}}
@string{im = {Indagationes Mathematicae}}
@string{inria = {Institut National de Recherche en Informatique et en Automatique}}
@string{ipl = {Information Processing Letters}}
@string{iria = {Institut de Recherche en Informatique et en Automatique}}
@string{ja = {Journal of Algorithms}}
@string{jacm = {Journal of the ACM}}
@string{jam = {Journal d'Analyse Math{\'e}matique}}
@string{jams = {Journal of the American Mathematical Society}}
@string{jamsa = {Journal of Applied Mathematics and Stochastic Analysis}}
@string{jap = {Journal of Applied Probability}}
@string{jaums = {Journal of the Australian Mathematical Society}}
@string{jcam = {Journal of Computational and Applied Mathematics}}
@string{jcp = {Journal of Computational Physics}}
@string{jcss = {Journal of Computer and System Sciences}}
@string{jct = {Journal of Combinatorial Theory}}
@string{jcta = {Journal of Combinatorial Theory, {\rm {S}eries {A}}}}
@string{jctb = {Journal of Combinatorial Theory, {\rm {S}eries {B}}}}
@string{jlms = {Journal of the London Mathematical Society}}
@string{jmaa = {Journal of Mathematical Analysis and Applications}}
@string{jmp = {Journal of Mathematical Physics}}
@string{jmpa = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}}
@string{jnt = {Journal of Number Theory}}
@string{jpa = {Journal of Physics {\rm {S}eries {A}}}}
@string{jsc = {Journal of Symbolic Computation}}
@string{jsiam = {Journal of the Society for Industrial and Applied Mathematics}}
@string{jsl = {Journal of Symbolic Logic}}
@string{jtnb = {Journal de Th{\'e}orie des Nombres de Bordeaux}}
@string{labri = {Laboratoire Bordelais de Recherche en Informatique}}
@string{lmc = {Laboratoire de Mod{\'e}lisation et Calcul. IMAG}}
@string{lncs = {Lecture Notes in Computer Science}}
@string{lnm = {Lecture Notes in Mathematics}}
@string{lri = {Laboratoire de Recherche en Informatique, Universit{\'e} de Paris XI}}
@string{ma = {Mathematische Annalen}}
@string{mc = {Mathematics of Computation}}
@string{mi = {Mathematical Intelligencer}}
@string{mm = {Math. Magazine}}
@string{mor = {Mathematics of Operations Research}}
@string{mpcps = {Mathematical Proceedings of the Cambridge Philosophical Society}}
@string{msm = {M{\'e}morial des Sciences Math{\'e}matiques}}
@string{mst = {Mathematical Systems Theory}}
@string{mt = {Maple Technical Newsletter}}
@string{mz = {Mathematische Zeitschrift}}
@string{na = {Numerical Algorithms}}
@string{nams = {Notices of the AMS}}
@string{nm = {Numerische Mathematik}}
@string{or = {Operations Research}}
@string{pams = {Proceedings of the American Mathematical Society}}
@string{pcps = {Proceedings of the Cambridge Philosophical Society}}
@string{peis = {Probability in the Engineering and Informational Sciences}}
@string{pjm = {Pacific Journal of Mathematics}}
@string{plms = {Proceedings of the London Mathematical Society}}
@string{plms2 = {Proceedings of the London Mathematical Society, {\rm Series~2}}}
@string{pnasusa = {Proceedings of the National Academy of Sciences of the USA}}
@string{prams = {Proceedings of the American Mathematical Society}}
@string{prsla = {Proceedings of the Royal Society. London. Series A.}}
@string{ptrf = {Probability Theory and Related Fields}}
@string{qjmo = {Quarterly Journal of Mathematics, Oxford Series}}
@string{rairotia = {RAIRO Theoretical Informatics and Applications}}
@string{rsa = {Random Structures \& Algorithms}}
@string{sam = {Studies in Applied Mathematics}}
@string{siamadm = {SIAM Journal on Algebraic and Discrete Methods}}
@string{siamam = {SIAM Journal on Applied Mathematics}}
@string{siamdm = {SIAM Journal on Discrete Mathematics}}
@string{siamma = {SIAM Journal on Mathematical Analysis}}
@string{siamna = {SIAM Journal on Numerical Analysis}}
@string{siamnum = {SIAM Journal on Numerical Analysis}}
@string{sicomp = {SIAM Journal on Computing}}
@string{sigsam = {SIGSAM Bulletin}}
@string{ssmh = {Studia Scientiarum Mathematicarum Hungarica}}
@string{steklov = {Proceedings of the Steklov Institute of Mathematics}}
@string{tams = {Transactions of the American Mathematical Society}}
@string{tcs = {Theoretical Computer Science}}
@string{tcsa = {Theoretical Computer Science, Series A}}
@string{tcsb = {Theoretical Computer Science, Series B}}
@string{toms = {ACM Transactions on Mathematical Software}}
@string{tpa = {Theory of Probability and Its Applications}}
@string{trams = {Transactions of the American Mathematical Society}}
@string{tsi = {Technique et Science Informatiques}}
@string{uqam = {Universit{\'e} du Qu{\'e}bec {\`a} Montr{\'e}al}}
@string{zam = {Zentralinstitut f{\"u}r Angewandte Mathematik}}
@string{zw = {Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie}}
@inproceedings{DuFlLoSc02,
Author = {Duchon, Philippe and Flajolet, Philippe and Louchard, Guy and Schaeffer, Gilles},
Booktitle = {Automata, Languages, and Programming},
Date-Added = {2006-06-20 10:58:49 +0200},
Date-Modified = {2006-06-20 10:58:49 +0200},
Editor = {P. Widmayer et al.},
Note = {Proceedings of the 29th ICALP Conference, Malaga, July 2002.},
Number = {2380},
Pages = {501--513},
Publisher = {Springer Verlag},
Series = {Lecture Notes in Computer Science},
Title = {Random Sampling from {B}oltzmann Principles},
Year = 2002}
@article{Vallee01,
Author = {Vall{\'e}e, Brigitte},
Date-Added = {2006-06-20 10:57:09 +0200},
Date-Modified = {2006-06-20 10:57:09 +0200},
Journal = {Algorithmica},
Number = {1/2},
Pages = {262--306},
Title = {Dynamical Sources in Information Theory: Fundamental Intervals and Word Prefixes},
Volume = 29,
Year = 2001}
@inproceedings{DaMiPuRo99,
Address = {Ulm},
Author = {Dantzer, Jean-Fran\c{c}ois and Mitrani, Isi and Puhalskii, Anatolii and Robert, Philippe},
Booktitle = {INFORMS AP99},
Date-Added = {2006-06-20 10:54:44 +0200},
Date-Modified = {2006-06-20 13:25:12 +0200},
Editor = {Volker Schmidt},
Month = {Juillet},
Title = {Large Scale and Heavy Traffic Asymptotics for Systems with Unreliable Servers},
Year = 1999}
@inproceedings{BaBoDeFlGaGo99,
Author = {Banderier, Cyril and Bousquet-M\'elou, Mireille and Denise, Alain and Flajolet, Philippe and Gardy, Dani\`ele and Gouyou-Beauchamps, Dominique},
Booktitle = {Formal Power Series and Algebraic Combinatorics},
Date-Added = {2006-06-20 10:54:44 +0200},
Date-Modified = {2006-06-20 13:43:33 +0200},
Editor = {C. Mart{\'\i}nez, M. Noy, O. Serra},
Note = {Proceedings of FPSAC'99, Universitat Polit\`ecnica de Catalunya. Version pr\'eliminaire dans le rapport de recherche INRIA \#3661},
Pages = {40--52},
Title = {On Generating Functions of Generating Trees},
Year = 1999}
@inproceedings{Regnier98a,
Author = {R{\'e}gnier, M.},
Booktitle = {RECOMB'98},
Date-Added = {2006-06-20 10:52:42 +0200},
Date-Modified = {2006-06-20 10:52:42 +0200},
Publisher = {ACM},
Title = {A {U}nified {A}pproach to {W}ord {S}tatistics},
Year = 1998}
@proceedings{FlSz97b,
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 10:51:18 +0200},
Editor = {Philippe Flajolet and Wojtek Szpankowski},
Note = {Special issue of the the journal, 302 pages.},
Publisher = {John Wiley},
Series = {Random Structures and Algorithms},
Title = {Average--Case Analysis of Algorithms},
Volume = {10(1--2)},
Year = 1997}
@phdthesis{Nicodeme97b,
Author = {Nicod\`eme, P.},
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 13:30:01 +0200},
Month = sep,
School = {Universit\'e {P}aris {V}{I}{I}},
Title = {Alignement avec des {F}amilles de {S}\'equences {P}rot\'eiques},
Type = {Th{\`e}se de Doctorat},
Year = 1997}
@inproceedings{NiSt97,
Author = {Nicod\`eme, P. and Steyaert, J.-M.},
Booktitle = {Fifth International Conference on Intelligent Systems for Molecular Biology},
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 13:30:08 +0200},
Pages = {210--213},
Publisher = {{AAAI} Press},
Title = {Selecting Optimal Oligonucleotide Primers for Multiplex {P}{C}{R}},
Year = 1997}
@article{FlSz97,
Author = {Flajolet, Philippe and Szpankowski, Wojtek},
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 10:51:19 +0200},
Journal = {Random Structures and Algorithms},
Month = jan,
Number = {1--2},
Pages = {1--3},
Title = {Analysis of Algorithms},
Volume = {10},
Year = 1997}
@article{Flajolet97a,
Author = {Flajolet, Philippe},
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 10:51:19 +0200},
Journal = {SIAM Review},
Keywords = {analysis of algorithms},
Month = jun,
Number = 2,
Pages = {341--345},
Title = {Review of {M}icha {H}ofri's book ``{{\em {A}nalysis of {A}lgorithms}}''},
Volume = 39,
Year = 1997}
@article{MaReSm97,
Author = {{M}ahmoud, H. and R{\'e}gnier, M. and {S}mythe, R.},
Date-Added = {2006-06-20 10:51:18 +0200},
Date-Modified = {2006-06-20 10:51:19 +0200},
Journal = {Random Structures and Algorithms},
Pages = {169--186},
Title = {Analysis of {B}oyer-{M}oore-{H}orspool {S}tring-{M}atching {H}euristic},
Volume = 10,
Year = {1997}}
@phdthesis{Dumas01,
Author = {Dumas, V.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:25:45 +0200},
Key = {Ergodicity},
Month = dec,
School = {\'Ecole polytechnique},
Title = {Approches fluides pour la stabilit\'e et l'instabilit\'e de r\'eseaux de files d'attente stochastiques \`a plusieurs classes de clients},
Type = {Th{\`e}se de Doctorat},
Year = 1995}
@misc{Lecomte96,
Author = {Lecomte, O.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:29:47 +0200},
Note = {M\'emoire de {DEA}, Supelec},
Title = {R\'eseaux sans fil: Adaptation d'{HiPeRLAN} type~1 sur {W}avelan},
Year = 1996}
@misc{Qayyum96,
Author = {Qayyum, A.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:19:08 +0200},
Note = {M\'emoire de {DEA}, Universit\'e de Paris-Sud},
Title = {Wireless Networks: {HiPeRLAN}},
Year = 1996}
@inproceedings{Flajolet96b,
Address = {Barcelona},
Author = {Flajolet, Philippe},
Booktitle = {Notes of the Seminar on Probabilistic Methods in Algorithmics},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 10:49:46 +0200},
Keywords = {lattice reduction, Gauss, continued fraction},
Note = {(Summary written by Nicola Galesi)},
Number = 5,
Pages = {44--53},
Series = {Quaderns, Centre de Recerca Matem{\`a}tica},
Title = {Analytic Variations on Quadtrees},
Year = 1996}
@inproceedings{ReTa96,
Author = {R{\'e}gnier, M. and Tahi, F.},
Booktitle = {Mathematical Analysis for Biological Sequences},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 10:49:46 +0200},
Note = {Proceedings of a workshop held in Trondheim, Norway},
Title = {Enumeration and Asymptotics in Computational Biology},
Year = 1996}
@inproceedings{Robert96,
Address = {Toulouse},
Author = {Robert, Ph.},
Booktitle = {Journ\'ees SMAI mod\'elisation al\'eatoire et statistique},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:31:01 +0200},
Month = sep,
Organization = {SMAI},
Title = {Synchronisation d'un syst\`eme de ressources et probl\`emes reli\'es},
Year = 1996}
@article{GuMo96,
Author = {Guillaume, D. and Morain, F.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:45:06 +0200},
Journal = {Applicable Algebra in Engineering, Communication and Computing},
Number = 4,
Pages = {263--277},
Title = {Building pseudoprimes with a large number of prime factors},
Volume = 7,
Year = 1996}
@article{JoMo95,
Author = {Joux, A. and Morain, F.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 10:49:46 +0200},
Journal = jnt,
Month = nov,
Number = 1,
Pages = {108--128},
Title = {Sur les sommes de caract{\`e}res li{\'e}es aux courbes elliptiques {\`a} multiplication complexe},
Volume = 55,
Year = 1995}
@article{Morain95a,
Author = {Morain, Fran\c{c}ois},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 13:46:19 +0200},
Journal = {Journal de Th{\'e}orie des Nombres de Bordeaux},
Pages = {255--282},
Title = {Calcul du nombre de points sur une courbe elliptique dans un corps fini~: aspects algorithmiques},
Volume = 7,
Year = 1995}
@article{MoShWi96,
Author = {Morain, F. and Shallit, J. and Williams, H. C.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 10:49:46 +0200},
Journal = {La revue du Mus{\'e}e des Arts et M{\'e}tiers},
Month = mar,
Pages = {14--19},
Title = {La machine {\`a} congruences},
Volume = 14,
Year = 1996}
@article{JaSz96,
Author = {Jacquet, Ph. and Szpankowski, W.},
Date-Added = {2006-06-20 10:49:46 +0200},
Date-Modified = {2006-06-20 10:49:46 +0200},
Journal = {Theoretical Computer Science},
Note = {68 pp.},
Title = {Analytical depoissonization and its applications},
Year = 1996}
@mastersthesis{Chyzak95,
Author = {Chyzak, Fr\'ed\'eric},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:07 +0200},
Month = jun,
School = {\'Ecole Polytechnique},
Title = {Manipulations formelles d'op\'erateurs lin\'eaires et calculs holonomes},
Type = {Rapport de stage de {DEA}},
Year = 1995}
@inproceedings{Gourdon95,
Author = {Gourdon, Xavier},
Booktitle = {Formal power series and algebraic combinatorics},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:07 +0200},
Editor = {B. Leclerc and J. Y. Thibon},
Note = {Proceedings SFCA'95},
Pages = {249--260},
Publisher = {Universit\'e de Marne-la-Vall\'ee},
Title = {Largest Component in Random Combinatorial Structures},
Year = 1995}
@inproceedings{CoMo94,
Author = {Couveignes, J.-M. and Morain, F.},
Booktitle = {Algorithmic Number Theory Symposium},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:07 +0200},
Editor = {L. Adleman and M.-D. Huang},
Note = {1st Algorithmic Number Theory Symposium - Cornell University, May 6-9, 1994},
Pages = {43--58},
Publisher = {Springer-Verlag},
Series = LNCS,
Title = {Schoof's algorithm and isogeny cycles},
Volume = 877,
Year = 1994}
@inproceedings{LeMo95,
Author = {Lercier, R. and Morain, F.},
Booktitle = {Advances in Cryptology -- EUROCRYPT '95},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:07 +0200},
Editor = {L. C. Guillou and J.-J. Quisquater},
Note = {International Conference on the Theory and Application of Cryptographic Techniques, Saint-Malo, France, May 1995, Proceedings},
Number = 921,
Pages = {79--94},
Series = LNCS,
Title = {Counting the number of points on elliptic curves over finite fields: strategies and performances},
Year = 1995}
@inproceedings{DaFlVa94,
Author = {Daud\'e, Herv\'e and Flajolet, Philippe and Vall\'ee, Brigitte},
Booktitle = {Algorithmic Number Theory Symposium},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:07 +0200},
Editor = {L. Adleman},
Keywords = {lattice reduction},
Note = {Proceedings of {\em ANTS'94}.},
Number = 877,
Pages = {144-158},
Series = LNCS,
Title = {An Analysis of the {G}aussian Algorithm for Lattice Reduction},
Year = 1994}
@inproceedings{Crapo95c,
Author = {Crapo, Henry and Rota, Gian-Carlo},
Booktitle = {Invariant Methods in Discrete and Computational Geometry},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 13:21:47 +0200},
Editor = {Neil White},
Pages = {197-222},
Publisher = {Kluwer Academic Publishers},
Title = {The Resolving Bracket},
Year = 1995}
@inproceedings{Crapo95b,
Author = {Crapo, Henry and Richter-Gebert, J{\"u}rgen},
Booktitle = {Invariant Methods in Discrete and Computational Geometry},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 13:21:11 +0200},
Editor = {Neil White},
Pages = {167-196},
Publisher = {Kluwer Academic Publishers},
Title = {Automatic Proving of Geometric Theorems},
Year = 1995}
@inproceedings{Crapo95d,
Author = {Crapo, Henry},
Booktitle = {Rota's ``Combinatorial Theory''},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 13:22:00 +0200},
Pages = {xix-xliii},
Publisher = {Birkha{\"u}ser Verlag},
Title = {Gian-Carlo Rota on Combinatorics},
Volume = 1,
Year = 1995}
@article{Nicodeme95,
Author = {Nicod\`eme, Pierre},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 13:30:22 +0200},
Journal = {Technique et Science Informatique},
Note = {Num\'ero sp\'ecial informatique et g\'enomes},
Number = 1,
Pages = {23--34},
Title = {A computer support for genotyping by multiplex {P}{C}{R}},
Volume = 14,
Year = 1995}
@article{ShWiMo95,
Author = {Shallit, J. and Williams, H. C. and Morain, F.},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:08 +0200},
Journal = {Mathematical Intelligencer},
Number = 3,
Pages = {41--47},
Title = {Discovery of a lost factoring machine},
Volume = 17,
Year = 1995}
@article{JMRo94,
Author = {Jean-Marie, A. and Robert, Ph.},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 13:29:34 +0200},
Journal = {Queueing Systems, Theory and Applications},
Key = {Limit Theorems},
Number = {1-2},
Pages = {129--136},
Title = {On the transient behavior of some single server queues},
Volume = {7},
Year = 1994}
@article{FlGo94,
Author = {Flajolet, Philippe and Golin, Mordecai},
Date-Added = {2006-06-20 10:48:07 +0200},
Date-Modified = {2006-06-20 10:48:08 +0200},
Journal = AI,
Keywords = {divide-and-conquer recurrence, Mellin transform, mergesort},
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Year = {1994}}
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Author = {Jacquet, Philippe and Szpankowski, Wojciech},
Date-Added = {2006-06-20 10:48:07 +0200},
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Year = 1995}
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Author = {Crapo, Henry},
Date-Added = {2006-06-20 10:48:07 +0200},
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Note = {Special issue ``The Mathematical Heritage of Sir William Rowan Hamilton'', 33 pages.},
Title = {Projective Configurations: their Invariants and Homology},
Year = 1995}
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Address = {Palaiseau, France},
Author = {Hwang, H.-K.},
Date-Added = {2006-06-20 10:46:19 +0200},
Date-Modified = {2006-06-20 13:27:37 +0200},
Month = dec,
School = {{\'E}cole Polytechnique},
Title = {Th{\'e}or{\`e}mes Limites pour les Structures Combinatoires et les Fonctions Arithm{\'e}tiques},
Type = {Th{\`e}se de Doctorat},
Year = 1994}
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Author = {Flajolet, Philippe and Lafforgue, Thomas},
Date-Added = {2006-06-20 10:46:19 +0200},
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Keywords = {singularity perturbation, bivariate asymptotic, limit law, quadtree},
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Pages = {151--175},
Title = {Search Costs in Quadtrees and Singularity Perturbation Asymptotics},
Volume = 12,
Year = 1994}
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Date-Added = {2006-06-20 10:46:19 +0200},
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Journal = am,
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Title = {Chirality and the Isotopy Classification of Skew Lines in Projective 3-Space},
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Address = {Paris},
Author = {Flajolet, Philippe},
Booktitle = {La Science au Pr\'esent},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
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Title = {La calculabilit{\'e} et ses limites},
Year = 1992}
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Date-Modified = {2006-06-20 10:44:26 +0200},
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Publisher = {Springer Verlag},
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Year = {1993}}
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Booktitle = {Algorithms---ESA'93},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Editor = {Thomas Lengauer},
Note = {Proceedings of the First European Symposium on Algorithms, Bad Honnef, September 1993.},
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Pages = {169--180},
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Title = {A Calculus of Random Generation},
Year = 1993}
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Booktitle = {CPM'93},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Note = {Proceedings 4th Symposium on Combinatorial Pattern Matching, Padova, Italy},
Pages = {215--227},
Publisher = {Springer-Verlag},
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Title = {A {U}nifying {L}ook at $d$-dimensional {P}eriodicities and {S}pace {C}overings},
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Author = {Fabret, F. and R{\'e}gnier, M. and Simon, E.},
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Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Note = {Proc. 19th International Conference on Very Large Databases, Dublin, Ireland},
Pages = {455--466},
Publisher = {M.~ Kaufmann},
Series = {IEEE},
Title = {An {A}daptative {A}lgorithm for {I}ncremental {E}valuation of {P}roduction {R}ules in {D}atabases},
Year = 1993}
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Author = {Breslauer, D.},
Booktitle = {ESA'93},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Editor = {Th. Lengauer},
Note = {In Proc. 1-st Annual European Symposium on Algorithms, Bad Honnef, Germany},
Pages = {61--72},
Publisher = {Springer-Verlag},
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Title = {Saving {C}omparisons in the {C}rochemore-{P}errin {S}tring {M}atching {A}lgorithm},
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Year = {1993}}
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Author = {Morain, Fran\c{c}ois},
Booktitle = {Eurocode 1992},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Editor = {P. Camion and P. Charpin and S. Harari},
Note = {Udine, novembre 1992},
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Author = {Flajolet, Philippe and Gardy, Dani{\`e}le and Thimonier, Lo{\"y}s},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
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Author = {Flajolet, Philippe and Gonnet, Gaston and Puech, Claude and Robson, J. M.},
Date-Added = {2006-06-20 10:44:26 +0200},
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Pages = {473-500},
Title = {Analytic Variations on Quadtrees},
Volume = 10,
Year = {1993}}
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Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 13:21:24 +0200},
Journal = {Topologie Structurale},
Pages = {391--400},
Title = {Autocontraintes planes et poly\`edres projet\'es I~: le motif de base},
Volume = {20},
Year = {1993}}
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Author = {Crapo, Henry},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 13:20:43 +0200},
Journal = {Advances in Mathematics},
Pages = {97-123},
Title = {On the Anick-Rota Resolution of the Bracket Ring},
Volume = {99},
Year = {1993}}
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Author = {Baeza-Yates, R. and R{\'e}gnier, M.},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
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Pages = {51--57},
Title = {Fast Algorithms for Two Dimensional and Multiple Pattern Matching},
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Year = 1993}
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Author = {Breslauer, D.},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Journal = {Information Processing Letters},
Pages = {345--347},
Title = {Testing superprimitivity},
Volume = {44},
Year = {1993}}
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Author = {Keller, Wilfrid and Morain, Fran\c{c}ois},
Date-Added = {2006-06-20 10:44:26 +0200},
Date-Modified = {2006-06-20 10:44:26 +0200},
Journal = {Abstracts of the AMS},
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Title = {The complete factorization of some large {M}ersenne composites},
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Year = 1992}
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Date-Added = {2006-06-20 10:44:26 +0200},
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Journal = {SIAM Journal on Discrete Mathematics},
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Pages = {197--213},
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Volume = 6,
Year = 1993}
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Author = {Atallah, M. and Jacquet, Ph. and Szpankowski, W.},
Date-Added = {2006-06-20 10:44:26 +0200},
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Year = 1993}
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Author = {Baeza-Yates, R. and R{\'e}gnier, M.},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
Journal = TCS,
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Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
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Keywords = {survey, analysis of algorithms, discrete mathematics},
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Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
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Date-Added = {2006-06-20 10:40:00 +0200},
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Date-Modified = {2006-06-20 10:40:00 +0200},
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Author = {Flajolet, Philippe},
Booktitle = {Automata, Languages and Programming},
Cv = {(Invited lecture.)},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
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Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
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Author = {Dumas, Philippe and Thimonier, Lo{\"y}s},
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Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
Editor = {P. Leroux and C. Reutenauer},
Note = {Proceedings of the 4th Colloquium},
Pages = {171-181},
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Date-Modified = {2006-06-20 10:40:00 +0200},
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Year = 1992}
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Booktitle = {Fourth Annual Symposium on Discrete Algorithms (SODA'93)},
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Year = 1993}
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Author = {Golin, Mordecai},
Booktitle = {Third Scandinavian Workshop on Algorithm Theory (SWAT '92)},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
Title = {Dynamic Closest Pairs: A Probabilistic Approach},
Year = 1992}
@inproceedings{Golin92b,
Author = {Golin, Mordecai},
Booktitle = {Fourth Annual Symposium on Discrete Algorithms (SODA '93)},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
Title = {Maxima in Convex Regions},
Year = 1992}
@inproceedings{AtJaSz92b,
Address = {Tucson},
Author = {Atallah, M. and Jacquet, Ph. and Szpankowski, W.},
Booktitle = {3rd Combinatorial Pattern Matching conference},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 13:18:34 +0200},
Month = {May},
Title = {Pattern matching with mismatches: a randomized algorithm and its analysis},
Year = 1992}
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Address = {Firenze},
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Date-Modified = {2006-06-20 13:28:37 +0200},
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Title = {A very simple algorithm for flow control on high speed networks, via LaPalice queueings},
Year = 1992}
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Address = {New York},
Author = {Morain, Fran\c{c}ois},
Booktitle = {ISSAC '92},
Date-Added = {2006-06-20 10:40:00 +0200},
Date-Modified = {2006-06-20 10:40:00 +0200},
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Title = {Easy numbers for the {E}lliptic {C}urve {P}rimality {P}roving algorithm},
Year = 1992}
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Author = {Crapo, Henry},
Date-Added = {2006-06-20 10:37:46 +0200},
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Note = {{\em Dans\/} Num\'ero sp\'ecial sur le th\`eme ``Th\'eorie des Invariants'', MR~90d:~51002},
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Title = {Invariant-Theoretic Methods in Scene Analysis and Structural Mechanics},
Volume = {11},
Year = {1991}}
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Date-Modified = {2006-06-20 13:15:27 +0200},
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Title = {Non-local and non-linear problems in mechanics of disordered systems: applications to granular media and rigidity problems},
Volume = {53},
Year = {1990}}
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Author = {Crapo, Henry},
Date-Added = {2006-06-20 10:37:46 +0200},
Date-Modified = {2006-06-20 13:18:00 +0200},
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Title = {On the Generic Rigidity of Structures in the Plane},
Year = {1991}}
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Author = {Morain, F.},
Date-Added = {2006-06-20 10:37:46 +0200},
Date-Modified = {2006-06-20 13:50:06 +0200},
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Year = 1990}
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Author = {Morain, F.},
Date-Added = {2006-06-20 10:37:46 +0200},
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Date-Added = {2006-06-20 10:37:46 +0200},
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Date-Modified = {2006-06-20 10:37:46 +0200},
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Year = 1991}
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Author = {Morain, F.},
Booktitle = {Advances in Cryptology -- EUROCRYPT '90},
Date-Added = {2006-06-20 10:37:46 +0200},
Date-Modified = {2006-06-20 10:37:46 +0200},
Editor = {{I. B. Damg\aa rd}},
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Year = 1991}
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Author = {Morain, F.},
Booktitle = {Advances in Cryptology -- EUROCRYPT '91},
Date-Added = {2006-06-20 10:37:46 +0200},
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Date-Modified = {2006-06-20 10:37:46 +0200},
Note = {Egalement disponible en Rapport de Recherche {\sc Inria} 1149},
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Title = {The {A}utomatic {C}omplexity {A}nalysis of {D}ivide-and-{C}onquer {A}lgorithms},
Year = 1991}
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Address = {Goehren, Germany},
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Month = may,
Title = {Complexity of recursive production rules execution},
Year = {1991}}
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Address = {Philadelphia},
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Date-Added = {2006-06-20 10:37:46 +0200},
Date-Modified = {2006-06-20 10:37:46 +0200},
Pages = {100-109},
Publisher = {SIAM Press},
Title = {The Analysis of Multidimensional Searching in Quad--Trees},
Year = {1991}}
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Address = {Orsay, France},
Author = {R{\'e}gnier, M.},
Date-Added = {2006-06-20 10:37:46 +0200},
Date-Modified = {2006-06-20 10:37:46 +0200},
School = {Univ. Paris-Sud},
Title = {Mots et motifs~: performances asymptotiques},
Type = {Habilitation {\`a} diriger des recherches},
Year = {1991}}
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Author = {Flajolet, P.},
Date-Added = {2006-06-20 10:31:19 +0200},
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Year = {1990}}
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Date-Modified = {2006-06-20 10:31:19 +0200},
Journal = SIAMDM,
Keywords = {asymptotics, generating functions},
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Volume = {3},
Year = {1990}}
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Author = {Flajolet, P. and Schott, R.},
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Author = {Crapo, Henry and Guyon, Etienne and Roux, St\'ephane and Hansen, Alex and Bideau, Daniel and Troadec, Jean-Paul},
Date-Added = {2006-06-20 10:31:19 +0200},
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Journal = {Reports on Progress in Physics},
Pages = {373-419},
Title = {Non-local and non-linear problems in mechanics of disordered systems: application to granular media and rigidity problems},
Volume = {53},
Year = {1990}}
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Author = {Coffman, E.G. and Fayolle, G. and Jacquet, Ph. and Robert, Ph.},
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Month = {May},
Pages = {141--146},
Title = {Largest-first sequential selection with a sum constraint},
Year = 1990}
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Volume = 36,
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Author = {Morain, F. and Olivos, J.},
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Title = {Speeding up the computations on an elliptic curve using addition-subtraction chains},
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Author = {Vitter, J. and Flajolet, P.},
Booktitle = {Handbook of Theoretical Computer Science},
Chapter = {9},
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Date-Modified = {2006-06-20 10:31:19 +0200},
Editor = {J. van Leeuwen},
Pages = {431--524},
Publisher = {North Holland},
Title = {Analysis of Algorithms and Data Structures},
Volume = {A: Algorithms and Complexity},
Year = {1990}}
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Author = {Allouche, J.--P. and Flajolet, P. and {Mend\`es France}, M.},
Booktitle = {Analytic Number Theory},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Editor = {K. Nagasaka and E. Fouvry},
Note = {Proceedings, Tokyo 1988},
Number = {1434},
Pages = {11-18},
Publisher = {Springer Verlag},
Series = LNM,
Title = {Algebraically independent formal power series: a language theory interpretation},
Year = {1990}}
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Author = {Flajolet, P. and Odlyzko, A. M.},
Booktitle = {Advances in Cryptology -- EUROCRYPT '89},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Editor = {J-J. Quisquater},
Keywords = {random mapping, survey, combinatorial models, cryptography},
Note = {Proceedings of {Eurocrypt'89}, Houthalen, Belgium, April 10--13, 1989},
Pages = {329--354},
Series = LNCS,
Title = {Random Mapping Statistics},
Volume = 434,
Year = {1990}}
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Author = {Flajolet, Philippe and Sipala, Paolo and Steyaert, Jean--Marc},
Booktitle = {Automata, Languages, and Programming},
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Note = {Proceedings of the 17th ICALP Conference, Warwick, July 1990},
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Series = LNCS,
Title = {Analytic Variations on the Common Subexpression Problem},
Volume = 443,
Year = {1990}}
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Author = {Vall\'ee, Brigitte and Flajolet, Philippe},
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Publisher = {IEEE Computer Society Press},
Title = {Gauss' Reduction Algorithm: An Average Case Analysis},
Year = {1990}}
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Booktitle = {Foundations of Software Technology and Theoretical Computer Science},
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Month = {{D\'ecembre}},
Note = {Proceedings of $9^{th}$ FFTTCS, Bangalore, India},
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Pages = {223-241},
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Series = LNCS,
Title = {Average case complexity analysis of {RETE} pattern match algorithm and average size of join in Databases},
Year = 1989}
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Author = {Morain, F.},
Booktitle = {Advances in Cryptology -- EUROCRYPT '89},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Editor = {J.-J. Quisquater},
Note = {Proc. Eurocrypt '89, Houthalen, April 10--13},
Pages = {626--635},
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Series = LNCS,
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Volume = 434,
Year = 1990}
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Author = {Baeza-Yates, R. and Gonnet, G. and R{\'e}gnier, M.},
Booktitle = {Proc. first SIAM-ACM Symposium on Discrete Algorithms},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Note = {SODA '90, San Francisco, January 22--24, 1990},
Pages = {328--343},
Publisher = {SIAM},
Title = {Analysis of {B}oyer-{M}oore-Type String Searching Algorithms},
Year = 1990}
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Author = {Baeza-Yates, R. and R{\'e}gnier, M.},
Booktitle = {SWAT'90},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Note = {Proc. Swedish Workshop on Algorithm Theory, Bergen, Norway},
Pages = {332--347},
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Series = LNCS,
Title = {Fast Algorithms for Two Dimensional and Multiple Pattern Matching},
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Author = {L.~Albert},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Month = {Octobre},
School = {Universit\'e de Paris--Sud, Orsay},
Type = {Th{\`e}se de Doctorat},
Title = {Quelques analyses de {complexit\'{e}} en moyenne sur les algorithmes de multi-filtrage, d'unification et de {requ\^{e}te} multiple},
Year = 1990}
@phdthesis{Morain90c,
Author = {Morain, Fran{\c{c}}ois},
Date-Added = {2006-06-20 10:31:19 +0200},
Date-Modified = {2006-06-20 10:31:19 +0200},
Month = {Septembre},
School = {Universit{\'e} Claude Bernard-Lyon {I}},
type = {Th{\`e}se de Doctorat},
Title = {Courbes elliptiques et tests de primalit{\'e}},
Year = 1990}
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Author = {Flajolet, P. and Kirschenhofer, P. and Tichy, R. F.},
Coden = {PTRFEU},
Date-Added = {2006-06-20 10:30:18 +0200},
Date-Modified = {2006-06-20 10:30:18 +0200},
Issn = {0178-8051},
Journal = {Probability Theory and Related Fields},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlKiTi88.pdf},
Mrclass = {11K06 (11K38)},
Mrnumber = {MR970475 (90a:11087)},
Mrreviewer = {Gerold S. Wagner},
Number = {1},
Pages = {139--150},
Title = {Deviations from uniformity in random strings},
Volume = {80},
Year = {1988}}
@incollection{Flajolet88a,
Address = {Rockville, Maryland},
Author = {Flajolet, P.},
Booktitle = {Trends in Theoretical Computer Science},
Chapter = {6},
Date-Added = {2006-06-20 10:30:18 +0200},
Date-Modified = {2006-06-20 10:30:18 +0200},
Editor = {Egon B{\"o}rger},
Note = {(Lecture Notes for {\em A Graduate Course in Computation Theory\/}, Udine, 1984)},
Pages = {225--304},
Publisher = {Computer Science Press},
Title = {Mathematical Methods in the Analysis of Algorithms and Data Structures},
Year = {1988}}
@inproceedings{FlGaTh88,
Author = {Flajolet, P. and Gardy, D. and Thimonier, L.},
Booktitle = {Automata, Languages and Programming},
Date-Added = {2006-06-20 10:30:18 +0200},
Date-Modified = {2006-06-20 10:30:18 +0200},
Editor = {Timo Lepist{\"o} and Arto Salomaa},
Note = {Proceedings of 15th ICALP Colloquium, Tempere, Finland, July 1988},
Pages = {239--253},
Publisher = {Springer-Verlag},
Series = LNCS,
Title = {Probabilistic Languages and Random Allocations},
Volume = 317,
Year = 1988}
@inproceedings{Flajolet88b,
Author = {Flajolet, P.},
Booktitle = {Journ{\'e}es Scientifiques et Prix U.A.P. 1985,1986,1987},
Date-Added = {2006-06-20 10:30:18 +0200},
Date-Modified = {2006-06-20 10:30:18 +0200},
Note = {(Text of Prize Award Lecture, 1986)},
Pages = {17--34},
Publisher = {Conseil Scientifique de l'UAP},
Title = {L'analyse d'algorithmes ou le risque calcul{\'e}},
Year = {1988}}
@inproceedings{Flajolet88d,
Author = {Flajolet, P.},
Booktitle = {PERFORMANCE'87},
Date-Added = {2006-06-20 10:30:18 +0200},
Date-Modified = {2006-06-20 10:30:18 +0200},
Editor = {P.-J. Courtois and G. Latouche},
Note = {(Invited lecture)},
Pages = {171--187},
Publisher = {Elsevier Science Publishers (North Holland)},
Title = {Random Tree Models in the Analysis of Algorithms},
Year = {1988}}
@article{Albert88,
Author = {Albert, Luc},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 10:28:56 +0200},
Journal = {Revue d'Intelligence Artificielle},
Pages = {7--40},
Title = {Pr{\'e}sentation et {\'e}valuation de la complexit{\'e} en moyenne d'algorithmes de filtrage dans les moteurs d'inf{\'e}rences ({R}ete et arbre d'unification)},
Volume = 2,
Year = 1988}
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Author = {Crapo, Henry and Cheung, Alan},
Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = {Journal Of Combinatorial Theory B},
Pages = {201-229},
Title = {On Relative Position in Extensions of Combinatorial Geometries},
Volume = {44},
Year = {1988}}
@article{Crapo90e,
Author = {Crapo, Henry},
Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = SIAMDM,
Title = {On the Generic Rigidity of Structures in the Plane},
Year = {1990}}
@article{FlFr89,
Author = {Flajolet, P. and Fran\c{c}on, J.},
Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = EJC,
Pages = {235--241},
Title = {Elliptic Functions, Continued Fractions and Doubled Permutations},
Volume = {10},
Year = {1989}}
@article{FlKnPi89,
Author = {Flajolet, P. and Knuth, D. E. and Pittel, B.},
Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = DM,
Pages = {167--215},
Title = {The first cycles in an evolving graph},
Volume = {75},
Year = {1989}}
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Author = {Gardy, D. and Flajolet, P. and Puech, C.},
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Journal = {Information Systems},
Number = 4,
Pages = {341--350},
Title = {Average cost of orthogonal range queries in multiattribute trees},
Volume = {14},
Year = 1989}
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Author = {Jacquet, P. and Szpankowski, W.},
Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = sicomp,
Number = {4},
Pages = {777--791},
Title = {Ultimate characterization of the burst response of an interval searching algorithm: a study of a functional equation},
Volume = {18},
Year = {1989}}
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Author = {Morain, F.},
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Pages = {225--229},
Title = {On the lcm of the differences of eight primes},
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Date-Added = {2006-06-20 10:28:56 +0200},
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Journal = IEEEIT,
Keywords = {size of tries, variance},
Number = {1},
Owner = {flajolet},
Pages = {203--205},
Title = {New Results on the Size of Tries},
Volume = {35},
Year = {1989}}
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Journal = RAIROTIA,
Keywords = {quicksort, limiting distributions, martingales},
Number = {3},
Owner = {flajolet},
Pages = {335--343},
Title = {The Limiting Distribution of Quicksort},
Volume = {23},
Year = {1989}}
@inproceedings{Crapo88b,
Address = {Minneapolis},
Author = {Crapo, Henry},
Booktitle = {Symbolic Computations in Geometry},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 13:19:52 +0200},
Organization = {Institure for Mathematics and its Applications},
Pages = {69--81},
Publisher = {University of Minnesota},
Series = {preprint series},
Title = {Towards Nonlinear {C}ayley Factorization},
Volume = 389,
Year = {1988}}
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Author = {Crapo, Henry and Laumond, Jean-Paul},
Booktitle = {Comptes rendus des Journ{\'e}es G{\'e}om{\'e}trie et Robotique, Toulouse, mai 1988},
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Publisher = {Springer-Verlag},
Series = LNCS,
Title = {{H}amilton Cycles in {D}elaunay Complexes},
Year = {1988}}
@inproceedings{Crapo89,
Author = {Crapo, Henry},
Booktitle = {Comptes rendus des Journ{\'e}es G{\'e}om{\'e}trie et Robotique, Toulouse, mai 1988},
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Publisher = {Springer-Verlag},
Series = LNCS,
Title = {Applications de l'Homologie G{\'e}om{\'e}trique},
Year = 1989}
@inproceedings{CuLaFl89,
Author = {Cunto, W. and Lau, G. and Flajolet, P.},
Booktitle = {Algorithms and Data Structures},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 10:28:56 +0200},
Editor = {F. Dehne and J-R. Sack and N. Santoro},
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Series = LNCS,
Title = {Analysis of {$kdt$}--trees: {$kd$}--trees improved by local reorganisations},
Volume = 382,
Year = {1989}}
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Author = {Flajolet, P. and Kirschenhofer, P. and Tichy, R. F.},
Booktitle = {Irregularities of Partitions},
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Date-Modified = {2006-06-20 10:28:56 +0200},
Editor = {G. Hal{\'a}sz and V. T. S{\'o}s},
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Publisher = {Springer Verlag},
Series = {Algorithms and Combinatorics},
Title = {Discrepancy of Sequences in Discrete Spaces},
Volume = {8},
Year = {1989}}
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Author = {Gardy, D. and Flajolet, P. and Puech, C.},
Booktitle = {Algorithms and Data Structures},
Date-Added = {2006-06-20 10:28:56 +0200},
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Editor = {F. Dehne and J-R. Sack and N. Santoro},
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Title = {On the performance of orthogonal range queries in multiattribute and doubly chained trees},
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Booktitle = {DE4},
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Date-Modified = {2006-06-20 13:30:45 +0200},
Editor = {IEEE},
Note = {Proceedings of the 4-th International Conference on Data Engineering, Los Angeles},
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Publisher = {Computer Society Press},
Title = {Trie Hashing Analysis},
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Note = {Proceedings Mathematical Foundations for Computer Science 89, Porubka, Poland},
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Date-Modified = {2006-06-20 10:28:56 +0200},
Note = {Proceedings of the workshop WADS'89, Ottawa, August 17-19, 1989},
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Note = {Proceedings des 6-{\`e}mes Journ{\'e}es Bases de Donn{\'e}es Avanc{\'e}es},
Pages = {131--154},
Publisher = {INRIA},
Title = {Efficient evaluation of rules in a {DBMS}},
Year = 1989}
@phdthesis{Jacquet89,
Author = {Jacquet, Ph.},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 10:28:56 +0200},
Month = {Novembre},
School = {Universit{\'e} de Paris--Sud},
type = {Th{\`e}se de 3e cycle},
Title = {Contribution de l'analyse d'algorithmes {\`a} l'{\'e}valuation de protocoles de communication},
Year = {1989}}
@techreport{HeMoSaSeVuZi89,
Author = {Herv\'e, J.-C. and Morain, F. and Salesin, D. and Serpette, B. and Vuillemin, J. and Zimmermann, P.},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 10:28:56 +0200},
Institution = {INRIA},
Month = {Avril},
Number = {1016},
Title = {BigNum: A Portable and Efficient Package for Arbitrary Precision Arithmetic},
Type = {Rapport de Recherche},
Year = {1989}}
@techreport{Zimmermann89,
Author = {Zimmermann, P.},
Date-Added = {2006-06-20 10:28:56 +0200},
Date-Modified = {2006-06-20 10:28:56 +0200},
Institution = INRIA,
Month = {January},
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Title = {Alas~: un syst{\`e}me d'analyse alg{\'e}brique},
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Date-Modified = {2006-06-20 10:24:54 +0200},
Mrclass = {51N05},
Mrnumber = {MR1011500},
Pages = {79--84},
Publisher = {Tech. Univ. Vienna},
Title = {Graphics programming in {P}ost{S}cript},
Year = {1988}}
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Address = {Boston, MA},
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Date-Modified = {2006-06-20 10:24:21 +0200},
Mrclass = {52A45 (52A25)},
Mrnumber = {MR937090},
Pages = {231--250},
Publisher = {Birkh\"auser Boston},
Series = {Design Sci. Collect.},
Title = {Convex polyhedra, {D}irichlet tessellations, and spider webs},
Year = {1988}}
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Date-Added = {2006-06-20 10:23:54 +0200},
Date-Modified = {2006-06-20 10:24:12 +0200},
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Issn = {0095-8956},
Journal = {J. Combin. Theory Ser. B},
Mrclass = {51D20 (05B35 06C10 51D25)},
Mrnumber = {MR930207 (89k:51009)},
Mrreviewer = {Nicolas Percsy},
Number = {2},
Pages = {201--229},
Title = {On relative position in extensions of combinatorial geometries},
Volume = {44},
Year = {1988}}
@Book{MoNi95,
author = {Fran{\c{c}}ois Morain and Jean-Louis Nicolas},
title = {Math{\'e}matiques \& {I}nformatique, {Q}uatorze probl{\`e}me corrig{\'e} pour l'enseignement sup{\'e}rieur},
publisher = {Vuibert},
year = 1995,
series = {Enseignement sup{\'e}rieur \& {I}nformatique}
}
@PhdThesis{Morain97b,
author = {F. Morain},
title = {Courbes elliptiques, arithm\'etique et corps finis},
school = {Universit{\'e} Paris 6},
year = 1997,
type = {M{\'e}moire d'habilitation}
}
@Article{Morain97,
author = {F. Morain},
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@InProceedings{Morain98a,
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year = 1998,
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year = 2000,
publisher = {{Logos Verlag}},
address = {Berlin}
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@Article{Nicodeme98,
author = {Pierre Nicod\`eme},
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@InProceedings{OlSe02,
author = {Ollivier, Fran\c{c}ois and Sedoglavic, Alexandre},
title = {Algorithmes efficaces pour tester
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year = 2002,
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address = {Nantes, France},
month = jul # {~8--10},
organization = {IEEE},
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@incollection{MeSe07,
Author = {Meunier, Fr\'ed\'eric and Seb{\"o}, Andras},
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@mastersthesis{Mezzarobba2007,
Author = {Mezzarobba, Marc},
Month = {octobre},
Note = {version 1.2, 89 pages},
School = {Master parisien de recherche en informatique},
Title = {G\'en\'eration automatique de proc\'edures num\'eriques pour les fonctions {D}-finies},
Type = {Rapport de stage},
Url = {http://algo.inria.fr/papers/pdf/Mezzarobba_MScThesisMPRI2007-1.2.pdf},
Year = {2007}}
@article{FuPoSc07,
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Date-Added = {2007-12-10 17:17:53 +0100},
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Keywords = {bijection; bipolar orientations; non-intersecting paths},
Pages = {283--287},
Title = {Bijective counting of plane bipolar orientations},
Title1 = {European Conference on Combinatorics, Graph Theory and Applications, European Conference on Combinatorics, Graph Theory and Applications},
Ty = {JOUR},
Url = {http://www.sciencedirect.com/science/article/B75GV-4PCHPN5-1R/2/84e28461fe6672d2c0b27589b5b04f9e},
Volume = {29},
Year = {2007},
Abstract = { We introduce a bijection between plane bipolar orientations with fixed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with some specific extremities. Writing [theta]ij for the number of plane bipolar orientations with (i+1) vertices and (j+1) faces, our bijection provides a combinatorial proof of the following formula due to Baxter:}}
@phdthesis{Fu07th,
Author = {Fusy, \'E.},
Date-Added = {2007-12-01 07:28:16 +0100},
Date-Modified = {2007-12-01 07:29:03 +0100},
Month = {June},
School = {\'Ecole Polytechnique},
Title = {Combinatoire des cartes planaires et applications algorithmiques},
url = {http://algo.inria.fr/papers/pdf/these_eric_fusy.pdf},
Year = {2007}}
@inproceedings{Flajolet07,
Author = {Flajolet, Philippe},
Booktitle = {ACM-SIAM Symposium on Discrete Algorithms (SODA)},
Date-Modified = {2007-12-10 16:59:29 +0100},
Pages = {137--148},
Publisher = {SIAM Press},
Title = {Analytic Combinatorics---A Calculus of Discrete Structures},
Year = {2007}}
@inproceedings{FlFuGaMe07,
Author = {Flajolet, Philippe and Fusy, {\'Eric} and Gandouet, Olivier and Meunier, {Fr\'ed\'eric}},
Booktitle = {Analysis of Algorithms 2007 (AofA07)},
Date-Added = {2007-05-05 14:25:46 +0200},
Date-Modified = {2007-05-05 14:57:35 +0200},
Editor = {Jacquet, Philippe},
Keywords = {probabilistic counting, Mellin transform, depoissonization, CV},
pages = {127--146},
Series = {Discrete Mathematics and Theoretical Computer Science Proceedings},
Title = {HyperLoglog: the analysis of a near-optimal cardinality estimation algorithm},
Year = {2007}}
@inproceedings{FlFuPi07,
Author = {Flajolet, Philippe and Fusy, {\'E}ric and Pivoteau, Carine},
Booktitle = {Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithmics and Combinatorics},
Date-Added = {2006-09-10 16:28:20 +0200},
Date-Modified = {2007-12-10 17:37:26 +0100},
Editor = {Appelgate, David},
Keywords = {Boltzmann model, CV, analytic combinatorics},
Local-Url = {file://localhost/Users/flajolet/Bib/ResearchLibrary/FlFuPi07.pdf},
Note = {Proceedings of the New Orleans Conference},
Pages = {201--211},
Publisher = {SIAM Press},
Title = {Boltzmann Sampling of Unlabelled Structures},
Year = {2007}}
@article{FlVe07,
Author = {Flajolet, Philippe and Vepstas, Linas},
Date-Added = {2007-05-05 14:32:22 +0200},
Date-Modified = {2007-12-10 17:28:38 +0100},
Journal = {Journal of Computational and Applied Mathematics},
Keywords = {zeta function, finite differences, CV},
Local-Url = {file://localhost/Users/flajolet/Bib/ResearchLibrary/FlVe07.pdf},
Title = {On Differences of Zeta Values},
arxiv = {abs/math/0611332},
volume = 220,
number ={1--2},
pages = {58--73},
month = oct,
Year = {2008}}
@article{BoFuKaVi07b,
Author = {Bodirsky, Manuel and Fusy, \'Eric and Kang, Mihyun and Vigerske, Stefan},
Date-Modified = {2007-12-10 16:55:34 +0100},
Journal = {Electronic Journal of Combinatorics},
Month = sep,
Note = {24 pages},
Number = {R66},
Title = {Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs },
Volume = {14},
Year = {2007}}
@inproceedings{BoFuKaVi07,
Author = {Bodirsky, Manuel and Fusy, {\'E}ric and Kang, Mihyun and Vigerske, Stefan},
Booktitle = {ACM-SIAM Symposium on Discrete Algorithms (SODA)},
Date-Added = {2006-12-11 18:21:39 +0100},
Date-Modified = {2007-12-10 17:01:16 +0100},
Pages = {356--365},
Title = {An unbiased pointing operator for unlabeled structures, with applications to counting and sampling},
Year = {2007}}
@inproceedings{Fusy07,
Author = {Fusy, {\'E}ric},
Booktitle = {Graph Drawing 2006},
Date-Added = {2006-12-11 18:21:39 +0100},
Date-Modified = {2007-12-10 17:08:58 +0100},
Note = {Karlsruhe, Germany, September 18--20, 2006},
Pages = {234--239},
Publisher = {Springer-Verlag},
Series = {Lecture Notes in Computer Science},
Title = {Straight-line drawing of quadrangulations},
Volume = {4372},
Year = {2007}}
@inproceedings{FuGi07,
Author = {Fusy, \'Eric and Giroire, Fr\'ed\'eric},
Booktitle = {Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithmics and Combinatorics},
Date-Added = {2006-12-11 19:10:40 +0100},
Date-Modified = {2007-12-10 17:37:26 +0100},
Editor = {Appelgate, David},
Note = {Proceedings of the New Orleans Conference},
Pages = {223--231},
Publisher = {SIAM Press},
Title = {Estimating the number of active flows in a data stream over a sliding window},
Year = {2007}}
@article {BoFuPi10,
AUTHOR = {Bodini, Olivier and Fusy, {\'E}ric and Pivoteau, Carine},
TITLE = {Random sampling of plane partitions},
JOURNAL = {Combin. Probab. Comput.},
FJOURNAL = {Combinatorics, Probability and Computing},
VOLUME = {19},
YEAR = {2010},
NUMBER = {2},
PAGES = {201--226},
arxiv = {abs/0712.0111},
DOI = {10.1017/S0963548309990332},
URL = {http://dx.doi.org/10.1017/S0963548309990332},
}@InProceedings{PaGoFl98,
author = "Daniel Panario and Xavier Gourdon and Philippe Flajolet",
title = "An analytic approach to smooth polynomials over finite
fields",
booktitle = "Algorithmic Number Theory Symposium (ANTS)",
series = LNCS,
volume = 1423,
publisher = "Springer Verlag",
year = "1998",
pages = "226--236",
editor = "J. P. Buhler",
keywords = "random polynomial, Dickman function"
}
@article{PaMaLiReNaDe02,
author = {Papatsenko, Dmitri A. and Makeev, Vsevolod J. and Lifanov, Alex P. and R{\'e}gnier, Mireille and Nazina, Anna G. and Desplan, Claude},
title = {Extraction of Functional Binding Sites from Unique Regulatory Regions: The {\em Drosophila\/} Early Developmental Enhancers},
journal = {Genome Research},
volume = 12,
number = 3,
pages = {470--481},
year = 2002
}
@mastersthesis{Panafieu2010,
Author = {Elie de Panafieu},
Month = {ao\^ut},
Note = {26 pages},
School = {\'Ecole Normale Sup\'erieure},
Title = {Complexit\'e et qualit\'e du d\'ecouplage obtenu par la m\'ethode du vecteur cyclique},
Type = {Rapport de stage},
Year = {2010}
}@mastersthesis{Pech2009,
Author = {Pech, Lucien},
Month = {novembre},
Note = {22 pages},
School = {\'Ecole Normale Sup\'erieure},
Title = {Algorithmes pour la sommation et l'int\'egration symboliques},
Type = {Rapport de stage},
Url = {http://algo.inria.fr/papers/pdf/Pech-2009-ASI.pdf},
Year = {2009}}
@Misc{Pivoteau05,
author = "Pivoteau, Carine",
title = "G\'en\'eration al\'eatoire et mod\`eles de {B}oltzmann",
year = 2005,
note = "M\'emoire de DEA, Universit\'e Paris VI"
}
@inproceedings{PivoteauSalvySoria2008,
Author = {Pivoteau, Carine and Salvy, Bruno and Soria, Mich{\`e}le},
Booktitle = {Algorithms, Trees, Combinatorics and Probabilities},
Date-Added = {2008-04-30 08:53:09 +0200},
Date-Modified = {2009-10-05 09:09:06 +0200},
Note = {Proceedings of the Fifth Colloquium on Mathematics and Computer Science. Blaubeuren, Germany. September 22-26, 2008},
Pages = {475--488},
Publisher = {Discrete Mathematics and Theoretical Computer Science},
Title = {Boltzmann Oracle for Combinatorial Systems},
Url = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAI0132},
Year = {2008},
Abstract = {Boltzmann random generation applies to well-defined systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.
}
}
@techreport{PivoteauSalvySoria2011,
Arxiv = {abs/1109.2688},
Author = {Pivoteau, Carine and Salvy, Bruno and Soria, Mich{\`e}le},
Date-Added = {2011-09-14 07:16:10 +0000},
Date-Modified = {2011-09-14 07:20:41 +0000},
Institution = {arXiv},
Keywords = {Species theory; analytic combinatorics; generating series; complexity.},
Title = {Algorithms for Combinatorial Systems},
Year = 2011,
Abstract = {We consider systems of recursively defined combinatorial structures. We present a quadratic iterative method solving these systems when they are well founded. From there, we deduce truncations of the corresponding generating series in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. This provides algorithms that are important subroutines in random generation.},
Note = {58 pages}
}
@article{Puyhaubert04,
author = {Puyhaubert, Vincent},
title = {Generating functions and the satisfiability threshold},
keywords = {First moment method, exponential generating functions, saddle-point bounds},
journal = {Discrete Mathematics and Theoretical Computer Science},
year = {2004},
volume = {6},
number = {2},
pages = {425--436},
url = {http://www.dmtcs.org/volumes/abstracts/dm060216.abs.html}
}
@PhdThesis{Puyhaubert05,
author = "Puyhaubert, Vincent",
title = "Mod{\`e}les d'urnes et ph{\'e}nom{\`e}nes de seuils en combinatoire analytique",
school = "{\'E}cole polytechnique",
year = "2005",
type = "Th{\`e}se de Doctorat",
url = {http://algo.inria.fr/papers/pdf/Puyhaubert2005.pdf}
}
@InProceedings{ReDe03b,
author = {M. R{\'e}gnier and A. Denise},
title = {Statistiques Extr\^emes sur les Mots},
year = 2003,
booktitle = "XXXV-\`emes Journ\'ees de Statistique",
volume ="2",
pages = "799--802",
note = "In Proceedings XXXV-\`emes Journ\'ees de Statistique, Lyon",
url = {http://algo.inria.fr/regnier/publis/ReDe03b.ps}
}
@article{ReDe04,
author = {Mireille R{\'e}gnier and Alain Denise},
title = {Rare events and Conditional Events on random strings},
year = {2004},
journal = {DMTCS},
volume= {6},
number = {2},
pages = {191--214},
url = {http://dmtcs.loria.fr/pspapers/dm060203.ps}
}
@Article{Regnier00b,
author = {M. R{\'e}gnier},
title = {A Unified Approach to Word Occurrences Probabilities},
journal = {Discrete Applied Mathematics},
year = 2000,
volume = 104,
number = 1,
pages = "259--280",
url = {http://algo.inria.fr/regnier/publis/Regnier00.ps},
note = {Special issue on Computational Biology}
}
@Inproceedings{Regnier01a,
author = "M. R{\'e}gnier",
title = "Complexity of {U}nusual {W}ords {C}ounting",
year = "2001",
booktitle = "JOBIM'00",
series = LNCS,
publisher = "Springer-Verlag",
volume = 2066,
pages = "101--117",
note = "Proceedings of JOBIM'00, Montpellier",
}
@InProceedings{Regnier04,
author = "Mireille R{\'e}gnier",
title = {Mathematical Tools for Regulatory Signals Extraction},
year = 2004,
booktitle = "Bioinformatics of Genome Regulation and Structure",
editor = "N. Kolchanov and R. Hofestaedt",
publisher = "Kluwer Academic Publisher",
pages = "61--70",
note = "Preliminary version at BGRS'02",
url = {http://algo.inria.fr/regnier/publis/Regnier2.doc}
}
@Misc{Regnier98b,
author = "M. R{\'e}gnier",
year = "1998",
title = "Generating {F}unctions in {C}omputational {B}iology",
note = "Invited to MABS'97"
}
@InProceedings{ReLiMa00,
author = "M. R{\'e}gnier and A. Lifanov and V. Makeev",
title = "Three Variations on Word Counting",
booktitle = "GCB'00",
year = "2000",
pages = "75--82",
publisher = "Logos-Verlag",
editors ="Bornberg-Bauer and Rost and Stoye and Vingron",
note = "Proceedings German Conference on Bioinformatics, Heidelberg"
}
@InProceedings{ReMo00,
author = "M. R{\'e}gnier and L. Mouchard",
title = "Periods and quasiperiods characterization",
booktitle = "CPM'00",
year = 2000,
pages = "388--396",
series = LNCS,
publisher = "Springer-Verlag",
volume = 1848,
note = "Proc. 11-th Annual Symposium on Combinatorial Pattern Matching,
CPM'00, Montreal"
}
@InProceedings{ReRo96,
author = {Mireille R{\'e}gnier and Ladan Rostami},
title = {A Simple (but Optimal) 2D-Witness Algorithm},
booktitle = {Third South American Workshop on String Processing},
number = 4,
series = {International Informatics Series},
year = 1996,
pages = {243--256},
url = {http://algo.inria.fr/papers/other/witness.ps.gz}
}
@InProceedings{ReSz97a,
author = "Mireille R{\'e}gnier and Wojciech Szpankowski",
title = "On the Approximate Pattern Occurrences in a Text",
year = 1997,
booktitle = "Compression and {C}omplexity of {SEQUENCES} 1997",
editor = "IEEE Computer Society",
pages = "253--264",
note = "In Proceedings SEQUENCE'97,Positano, Italy",
url = {http://algo.inria.fr/papers/other/ReSz97a.ps.gz}
}
@InProceedings{ReSz98a,
author = {Mireille R{\'e}gnier and Wojtek Szpankowski},
title = {{C}omplexity of {S}equential {P}attern
{M}atching {A}lgorithms},
booktitle = {RANDOM'98},
number = 1518,
series = {Lecture Notes in Computer Science},
year = 1998,
publisher = {Springer-Verlag},
pages = {187--199},
url = {http://algo.inria.fr/papers/other/ReSz98a.ps}
}
@Article{ReSz98b,
author = "Mireille R{\'e}gnier and Wojciech Szpankowski",
title = "On Pattern Frequency Occurrences in a Markovian Sequence?",
year = 1998,
journal = "Algorithmica",
volume = 22,
number = {4},
pages = {631--649},
note = "This paper was presented in part at the 1997 {\it
International Symposium on Information Theory}, Ulm,
Germany.",
url = {http://algo.inria.fr/papers/other/ReSz97b.ps.gz}
}
@InProceedings{ReSz98c,
author = "Mireille R{\'e}gnier and Wojciech Szpankowski",
title = "On the Approximate Pattern Occurrences in a Text",
year = 1998,
booktitle = "Compression and {C}omplexity of {SEQUENCES} 1997",
publisher = "IEEE Computer Society",
pages = "253--264",
note = "Proceedings SEQUENCE'97, Positano, Italy",
url = {http://algo.inria.fr/papers/other/ReSz97a.ps.gz}
}
@article{ReTa04,
author = "M. R{\'e}gnier and F. Tahi",
year = "2004",
title = "Generating Functions in Computational Biology",
journal = "Journal of Iranian Statistics",
url = {http://algo.inria.fr/regnier/publis/ReTa04.ps},
note = "Preliminary version at MABS'97; to appear"
}
@article{ReVa06,
author = "M. R{\'e}gnier and M. Vandenbogaert",
title = "Comparison of Statistical Significance Criteria",
year = "2006",
journal = {Journal of Bioinformatics and Computational Biology},
volume = "4",
number = "2",
pages ="537--551",
url = {http://algo.inria.fr/regnier/publis/ReVa05.ps}
}
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volume = 35,
pages = {x+368},
series = {Math{\'e}matiques et {A}pplications},
address = {Berlin},
month = {Octobre},
}
@Article{Robert98,
author = {Philippe Robert},
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processes},
journal = "Queueing Systems, Theory and Applications",
year = 1998,
volume = 29,
number = {2-4},
pages = "189--192"
}
@book{sagebook-1.0,
author = {Alexandre Casamayou and Guillaume Connan and Thierry Dumont
and Laurent Fousse and Fran{\c c}ois Maltey and Matthias Meulien and
Marc Mezzarobba and Cl{\'e}ment Pernet and Nicolas M. Thi{\'e}ry
and Paul Zimmermann},
year = {2010},
title = {Calcul math{\'e}matique avec Sage},
url = {http://sagebook.gforge.inria.fr/},
comment = {version 1.0}
}
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@article{GiLeSaYa07,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Giusti, Marc and Lecerf, Gr{\'e}goire and Salvy, Bruno and Yakoubsohn, Jean-Claude},
Date-Added = {2005-07-24 18:12:51 +0800},
Date-Modified = {2007-02-12 14:15:26 +0100},
Doi = {10.1007/s10208-004-0159-5},
Journal = {Foundations of Computational Mathematics},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GiLeSaYa06.pdf},
Month = feb,
Number = {1},
Pages = {1--58},
Title = {On Location and Approximation of Clusters of Zeroes: Case of Embedding Dimension One},
Volume = {7},
Year = {2007},
Abstract = { Isolated multiple zeros or clusters of zeros of analytic maps with
several variables are known to be difficult to locate and
approximate. This article is in the vein of the $\alpha$-theory,
initiated by M.~Shub and S.~Smale in the beginning of the eighties.
This theory restricts to simple zeros, i.e., where the map has
corank zero. In this article we deal with situations where the
analytic map has corank one at the multiple isolated zero, which has
embedding dimension one in the frame of deformation theory. These
situations are the least degenerate ones and therefore most likely
to be of practical significance. More generally, we define clusters
of embedding dimension one. We provide a criterion for locating such
clusters of zeros and a fast algorithm for approximating them, with
quadratic convergence. In case of a cluster with positive diameter
our algorithm stops at a distance of the cluster which is about its
diameter.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10208-004-0159-5}}
@article{GoSa08,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Gomez, Claude and Salvy, Bruno},
Date-Added = {2006-03-01 07:04:45 +0100},
Date-Modified = {2008-04-24 11:39:18 +0200},
Journal = {Les Techniques de l'Ing{\'e}nieur},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GoSa06.pdf},
Pages = {1--20},
Title = {Calcul Formel},
Volume = {Dossier AF1460},
Year = {2008},
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@article{BoFlSaSc06,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Flajolet, Philippe and Salvy, Bruno and Schost, {\'E}ric},
Date-Added = {2005-09-28 10:52:57 +0200},
Date-Modified = {2006-02-25 09:18:29 +0100},
Doi = {10.1016/j.jsc.2005.07.001},
Journal = {Journal of Symbolic Computation},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoFlSaSc06.pdf},
Month = jan,
Number = {1},
Pages = {1--29},
Title = {Fast Computation of Special Resultants},
Volume = {41},
Year = {2006},
Abstract = {We propose fast algorithms for computing composed products and
composed sums, as well as diamond products of univariate
polynomials. These operations correspond to special multivariate
resultants, that we compute using power sums of roots of polynomials,
by means of their generating series.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jsc.2005.07.001}}
@article{GiLeSaYa05,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Giusti, Marc and Lecerf, Gr{\'e}goire and Salvy, Bruno and Yakoubsohn, Jean-Claude},
Date-Added = {2005-06-13 15:25:37 +0200},
Date-Modified = {2006-03-04 13:29:58 +0100},
Doi = {10.1007/s10208-004-0144-z},
Journal = {Foundations of Computational Mathematics},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GiLeSaYa05.pdf},
Month = jul,
Number = {3},
Pages = {257--311},
Title = {On Location and Approximation of Clusters of Zeroes of Analytic Functions},
Volume = {5},
Year = {2005},
Abstract = {At the beginning of the 1980s, M. Shub and S. Smale developed a quantitative analysis of Newton's method for multivariate analytic maps. In particular, their $\alpha$-theory gives an effective criterion that ensures safe convergence to a simple isolated zero. This criterion requires only information concerning the map at the initial point of the iteration. Generalizing this theory to multiple zeros and clusters of zeros is still a challenging problem. In this paper we focus on one complex variable function. We study general criteria for detecting clusters and analyze the convergence of Schr{\"o}der's iteration to a cluster. In the case of a multiple root, it is well known that this convergence is quadratic. In the case of a cluster with positive diameter, the convergence is still quadratic provided the iteration is stopped sufficiently early. We propose a criterion for stopping this iteration at a distance from the cluster which is of the order of its diameter.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10208-004-0144-z}}
@inproceedings{Salvy05,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno},
Booktitle = {ISSAC'05},
Date-Added = {2005-07-24 10:07:57 +0800},
Date-Modified = {2006-02-25 09:19:22 +0100},
Doi = {10.1145/1073884.1073886},
Editor = {Kauers, Manuel},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/Salvy05.pdf},
Note = {Abstract for an invited talk. Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, Beijing, July 2005.},
Pages = {2--3},
Publisher = {ACM Press},
Title = {D-Finiteness: Algorithms and Applications},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1073884.1073886}}
@article{ChMiSa05,
Arxiv = {abs/math/0310132},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Chyzak, Fr\'ed\'eric and Mishna, Marni and Salvy, Bruno},
Date-Added = {2005-06-13 15:22:59 +0200},
Date-Modified = {2008-04-24 11:38:10 +0200},
Doi = {10.1016/j.jcta.2005.01.001},
Journal = {Journal of Combinatorial Theory, Series A},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/ChMiSa05.pdf},
Month = oct,
Note = {Extended version of an article published in the proceedings of the 14th Conference of Formal Power Series and Algebraic Combinatorics FPSAC'02, Melbourne, July 2002},
Number = {1},
Pages = {1--43},
Title = {Effective Scalar Products of {D}-finite Symmetric Functions},
Volume = {112},
Year = {2005},
Abstract = {Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the resulting generating functions are D-finite. We extend Gessel's work by providing algorithms that compute differential equations, these generating functions satisfy in the case they are given as a scalar product of symmetric functions in Gessel's class. Examples of applications to k-regular graphs and Young tableaux with repeated entries are given. Asymptotic estimates are a natural application of our method, which we illustrate on the same model of Young tableaux. We also derive a seemingly new formula for the Kronecker product of the sum of Schur functions with itself.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcta.2005.01.001}}
@article{FlGeSa05,
Arxiv = {abs/math/0501379},
Author = {Flajolet, Philippe and Gerhold, Stefan and Salvy, Bruno},
Date-Added = {2005-06-13 15:28:14 +0200},
Date-Modified = {2008-04-24 11:38:16 +0200},
Journal = {The Electronic Journal of Combinatorics},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlGeSa05.pdf},
Month = apr,
Note = {A2, 16 pages},
Number = 2,
Title = {On the non-holonomic character of logarithms, powers, and the nth prime function},
Url = {http://www.combinatorics.org/Volume_11/PDF/v11i2a2.pdf},
Volume = 11,
Year = 2005,
Abstract = {We establish that the sequences formed by logarithms and by ``fractional''
powers of integers, as
well as
the sequence of prime numbers, are non-holonomic, thereby answering three
open problems of Gerhold [\emph{El. J. Comb.} {\bf 11} (2004), R87].
Our proofs depend on basic complex analysis, namely
a conjunction of
the Structure Theorem for singularities of solutions to
linear differential equations and of an Abelian theorem.
A brief discussion is offered regarding the scope of
singularity-based methods and several naturally
occurring sequences are proved to be non-holonomic.},
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Bdsk-Url-1 = {http://www.combinatorics.org/Volume_11/PDF/v11i2a2.pdf}}
@inproceedings{BaFaSaYa05,
Author = {Bardet, M. and Faug{\`e}re, J.-C. and Salvy, B. and Yang, B.-Y.},
Booktitle = {MEGA'05},
Date-Added = {2005-06-13 15:26:40 +0200},
Date-Modified = {2006-01-21 12:34:41 +0100},
Note = {Eighth International Symposium on Effective Methods in Algebraic Geometry, Porto Conte, Alghero, Sardinia (Italy), May 27th -- June 1st},
Title = {Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems},
Year = 2005,
Abstract = { We compute the asymptotic expansion of the degree of regularity for
overdetermined semi-regular sequences of algebraic equations. This
degree implies bounds for the generic complexity of Gr{\"o}bner bases
algorithms, in particular Faug{\`e}re's $F_5$ algorithm. Bounds
can also be derived for the XL family of algorithms used
by the cryptographic community.
}}
@inproceedings{BoClSa05,
Address = {New York},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Cluzeau, Thomas and Salvy, Bruno},
Booktitle = {ISSAC'05},
Date-Added = {2005-06-13 15:27:29 +0200},
Date-Modified = {2006-02-25 09:19:33 +0100},
Doi = {10.1145/1073884.1073893},
Editor = {Kauers, Manuel},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoClSa05.pdf},
Note = {Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, July 2005, Beijing, China.},
Pages = {45--52},
Publisher = {ACM Press},
Title = {Fast Algorithms for Polynomial Solutions of Linear Differential Equations},
Year = 2005,
Abstract = {We investigate polynomial solutions of homogeneous linear differential equations with coefficients that are polynomials with integer coefficients. The problems we consider are the existence of nonzero polynomial solutions, the determination of the dimension of the vector space of polynomial solutions, the computation of a basis of this space. Previous algorithms have a bit complexity that is at least quadratic in the largest integer valuation $N$ of formal Laurent series solutions at infinity, even for merely detecting the existence of nonzero polynomial solutions. We give a deterministic algorithm that computes a compact representation of a basis of polynomial solutions in $O(N\log^3N)$ bit operations. We also give a probabilistic algorithm that computes the dimension of the space of polynomial solutions in $O(N\log^2N)$ bit operations. In general, the integer $N$ is not polynomially bounded in the bit size of the input differential equation. We isolate a class of equations for which detecting nonzero polynomial solutions can be performed in polynomial complexity. We discuss implementation issues and possible extensions.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1073884.1073893}}
@inproceedings{BoLeSaScWi04,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Lecerf, Gr{\'e}goire and Salvy, Bruno and Schost, {\'E}ric and Wiebelt, Bernd},
Booktitle = {Symbolic and Algebraic Computation},
Date-Added = {2005-06-13 15:29:11 +0200},
Date-Modified = {2006-02-25 09:19:44 +0100},
Doi = {10.1145/1005285.1005294},
Editor = {Gutierrez, J.},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoLeSaScWi04.pdf},
Note = {Proceedings of ISSAC'04, Santander, July 2004},
Pages = {42--49},
Publisher = {ACM Press},
Title = {Complexity Issues in Bivariate Polynomial Factorization},
Year = 2004,
Abstract = {Many polynomial factorization algorithms rely on Hensel lifting and factor recombination. For bivariate polynomials we show that lifting the factors up to a precision linear in the total degree of the polynomial to be factored is sufficient to deduce the recombination by linear algebra, using trace recombination. Then, the total cost of the lifting and the recombination stage is subquadratic in the size of the dense representation of the input polynomial. Lifting is often the practical bottleneck of this method: we propose an algorithm based on a faster multi-moduli computation for univariate polynomials and show that it saves a constant factor compared to the classical multifactor lifting algorithm.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1005285.1005294}}
@article{FlSaSc04,
Author = {Flajolet, Philippe and Salvy, Bruno and Schaeffer, Gilles},
Date-Added = {2005-06-13 15:29:59 +0200},
Date-Modified = {2006-01-19 23:31:55 +0100},
Journal = {The Electronic Journal of Combinatorics},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlSaSc04.pdf},
Month = may,
Note = {30 pages},
Number = 1,
Owner = {bs},
Pages = {R34},
Title = {Airy Phenomena and Analytic Combinatorics of Connected Graphs},
Url = {http://www.combinatorics.org/Volume_11/PDF/v11i1r34.pdf},
Volume = 11,
Year = 2004,
Abstract = {Until now, the enumeration of connected graphs has been dealt with
by probabilistic methods,
by special combinatorial decompositions
or by somewhat indirect formal series manipulations.
We show here that it is possible to make analytic sense of the
divergent series that expresses the generating function of connected
graphs.
As a consequence, it becomes possible to derive analytically
known
enumeration results
using only first principles of combinatorial analysis and
straight asymptotic analysis---specifically, the
saddle-point method. In this perspective, the enumeration of connected
graphs by excess (of
number of edges over number of vertices)
derives from a simple saddle-point analysis.
Furthermore, a refined analysis based on coalescent saddle points
yields complete asymptotic expansions for the number of graphs of
fixed excess, through an explicit connection with Airy functions.},
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Bdsk-Url-1 = {http://www.combinatorics.org/Volume_11/PDF/v11i1r34.pdf}}
@inproceedings{BaFaSa04,
Author = {Bardet, Magali and Faug\`ere, Jean-Charles and Salvy, Bruno},
Booktitle = {International Conference on Polynomial System Solving},
Date-Added = {2005-07-24 18:12:51 +0800},
Date-Modified = {2006-01-19 23:28:54 +0100},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BaFaSa04.pdf},
Month = nov,
Note = {Proceedings of a conference held in Paris, France in honor of Daniel Lazard},
Pages = {71--74},
Title = {On the Complexity of {G}r{\"o}bner basis computation of Semi-regular Overdetermined algebraic equations},
Url = {http://www-calfor.lip6.fr/ICPSS/papers/43BF/43bf.htm},
Year = 2004,
Abstract = {We extend Macaulay's notion of regular sequence to overdetermined system of algebraic equations. We study generic properties of Gr{\"o}bner bases and analyse precisely the behavior of Faug{\`e}re's F5 algorithm. Sharp asymptotic estimates of the degree of regularity are given. },
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Bdsk-Url-1 = {http://www-calfor.lip6.fr/ICPSS/papers/43BF/43bf.htm}}
@inproceedings{MeSa03,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Meunier, Ludovic and Salvy, Bruno},
Booktitle = {Symbolic and Algebraic Computation},
Date-Modified = {2006-03-14 10:23:45 +0100},
Doi = {10.1145/860854.860898},
Editor = {Sendra, J. R.},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/MeSa03.pdf},
Note = {Proceedings of ISSAC'03, Philadelphia, August 2003.},
Pages = {199--205},
Publisher = {ACM Press},
Title = {{ESF}: An Automatically Generated Encyclopedia of Special Functions},
Year = 2003,
Abstract = {We present our on-going work on the automatic generation of an encyclopedia of special functions on the web, called The Encyclopedia of Special Functions (ESF) http://algo.inria.fr/esf. All mathematical formul{\ae} in the ESF are computed, typeset and displayed without any human intervention. This is achieved by exploiting a collection of computer algebra algorithms in a systematic way, on top of a specially designed data structure for a class of special functions.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/860854.860898}}
@article{BoSaSc03,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bostan, Alin and Salvy, Bruno and Schost, {\'E}ric},
Date-Added = {2005-06-13 15:31:13 +0200},
Date-Modified = {2006-03-14 10:24:06 +0100},
Doi = {10.1007/s00200-003-0133-5},
Journal = {Applicable Algebra in Engineering, Communication and Computing},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BoSaSc03.pdf},
Number = 4,
Owner = {bs},
Pages = {239--272},
Title = {Fast Algorithms for Zero-Dimensional Polynomial Systems Using Duality},
Volume = 14,
Year = {2003},
Abstract = { Many questions concerning a zero-dimensional polynomial system can
be reduced to linear algebra operations in the quotient
algebra~$A=k[X_1,\dots,X_n]/I$, where~$I$ is the ideal generated
by the input system. Assuming that the multiplicative structure of
the algebra $A$ is (partly) known, we address the question of
speeding up the linear algebra phase for the computation of minimal
polynomials and rational parametrizations in $A$.
We present new formul{\ae}\ for the rational parametrizations,
extending those of Rouillier, and algorithms extending ideas
introduced by Shoup in the univariate case. Our approach is based on
the~$A$-module structure of the dual space~$\widehat{A}$. An
important feature of our algorithms is that we do not
require~$\widehat{A}$ to be free and of rank~1.
The complexity of our algorithms for computing the minimal
polynomial and the rational parametrizations are~$O(2^nD^{5/2})$
and~$O(n2^nD^{5/2})$ respectively, where~$D$ is the dimension
of~$A$. For fixed~$n$, this is better than algorithms based on
linear algebra except when the complexity of the available matrix
product has exponent less than~5/2.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00200-003-0133-5}}
@article{CoRoSa02,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Cori, Robert and Rossin, Dominique and Salvy, Bruno},
Date-Added = {2005-07-24 18:11:56 +0800},
Date-Modified = {2006-03-14 10:24:22 +0100},
Doi = {10.1016/S0304-3975(00)00397-2},
Journal = {Theoretical Computer Science},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/CoRoSa02.pdf},
Number = 1,
Pages = {1--15},
Title = {Polynomial Ideals for Sandpiles and their {G}r{\"o}bner Bases},
Volume = 276,
Year = 2002,
Abstract = {A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gr{\"o}bner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0304-3975(00)00397-2}}
@article{NiSaFl02,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Nicod{\`e}me, Pierre and Salvy, Bruno and Flajolet, Philippe},
Date-Added = {2005-07-24 18:11:56 +0800},
Date-Modified = {2006-03-14 10:24:14 +0100},
Doi = {10.1016/S0304-3975(01)00264-X},
Journal = {Theoretical Computer Science},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/NiSaFl02.pdf},
Note = {Extended version of an article published in the proceedings of 7th Annual European Symposium on Algorithms ESA'99, Prague, July 1999},
Number = 2,
Pages = {593--618},
Title = {Motif Statistics},
Volume = 287,
Year = 2002,
Abstract = {We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers ``motifs'' widely used in computational biology. Our approach is based on: (i) classical constructive results in automata and formal language theory; (ii) analytic combinatorics that is used for deriving asymptotic properties from generating functions; (iii) computer algebra in order to determine generating functions explicitly, analyse generating functions and extract coefficients efficiently. We provide constructions for overlapping or non-overlapping matches of a regular expression. A companion implementation produces: multivariate generating functions for the statistics under study; a fast computation of their Taylor coefficients which yields exact values of the moments with typical application to random texts of size 30,000; precise asymptotic formul{\ae} that allow predictions in texts of arbitrarily large sizes. Our implementation was tested by comparing predictions of the number of occurrences of motifs against the 7 megabytes amino acid database Procite. We handled more than 88% of the standard collection of Prodom motifs with our programs. Such comparisons help detect which motifs are observed in real biological data more or less frequently than theoretically predicted. },
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0304-3975(01)00264-X}}
@techreport{SaSh02,
Author = {Salvy, Bruno and Shackell, John},
Institution = {University of Kent, Canterbury},
Month = oct,
Number = {UKC/IMS/02/33},
Title = {Asymptotic Expansions with Oscillating Coefficients},
Type = {Research Report},
Year = 2002}
@techreport{Salvy01,
Author = {Salvy, Bruno},
Date-Added = {2005-07-24 18:10:55 +0800},
Date-Modified = {2006-01-19 23:41:42 +0100},
Institution = {Institut National de Recherche en Informatique et en Automatique},
Note = {14 pages},
Number = 4201,
Title = {Even-Odd Set Partitions, Saddle-Point Method and {W}yman Admissibility},
Type = {Research Report},
Url = {http://www.inria.fr/rrrt/rr-4201.html},
Year = 2001,
Abstract = {The reciprocal of the generating function of the Bell numbers enumerates the difference between numbers of set partitions with even and odd number of blocks. The asymptotic behaviour of this oscillatory sequence is obtained by a saddle-point analysis involving two conjugate saddle points. Technical details of the analysis are dealt with by appealing to Wyman's class of admissible functions.},
Bdsk-Url-1 = {http://www.inria.fr/rrrt/rr-4201.html}}
@article{GiLeSa01,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Giusti, Marc and Lecerf, Gr{\'e}goire and Salvy, Bruno},
Date-Modified = {2006-03-14 10:24:31 +0100},
Doi = {10.1006/jcom.2000.0571},
Journal = {Journal of Complexity},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GiLeSa01.pdf},
Month = mar,
Number = 1,
Pages = {154--211},
Title = {A {G}r{\"o}bner Free Alternative for Polynomial System Solving},
Volume = 17,
Year = 2001,
Abstract = {Given a system of polynomial equations and inequations with coefficients in the field of rational numbers, we show how to compute a geometric resolution of the set of common roots of the system over the field of complex numbers. A geometric resolution consists of a primitive element of the algebraic extension defined by the set of roots, its minimal polynomial, and the parametrizations of the coordinates. Such a representation of the solutions has a long history which goes back to Leopold Kronecker and has been revisited many times in computer algebra. We introduce a new generation of probabilistic algorithms where all the computations use only univariate or bivariate polynomials. We give a new codification of the set of solutions of a positive dimensional algebraic variety relying on a new global version of Newton's iterator. Roughly speaking the complexity of our algorithm is polynomial in some kind of degree of the system, in its height, and linear in the complexity of evaluation of the system. We present our implementation in the Magma system which is called Kronecker in homage to his method for solving systems of polynomial equations. We show that the theoretical complexity of our algorithm is well reflected in practice and we exhibit some cases for which our program is more efficient than the other available software.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jcom.2000.0571}}
@inproceedings{MeunierSalvy2001,
Author = {Meunier, Ludovic and Salvy, Bruno},
Booktitle = {Mathematical Knowledge Management},
Date-Added = {2005-07-24 18:11:05 +0800},
Date-Modified = {2009-10-05 09:12:13 +0200},
Note = {Proceedings MKM'01, Linz, September 2001. A more advanced version has appeared in~\cite{MeSa03}},
Title = {Automatically Generated Encyclopedia of Special Functions},
Url = {http://www.risc.uni-linz.ac.at/about/conferences/MKM2001/Proceedings/printed/meunier.ps},
Year = 2001,
Abstract = {We present our on-going work on creating an automatically generated encyclopedia of special functions. The aim is to exploit recent progress in computer algebra in order to synthesize web pages on special functions and provide some level of interactivity.
},
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Bdsk-Url-1 = {http://www.risc.uni-linz.ac.at/about/conferences/MKM2001/Proceedings/printed/meunier.ps}}
@article{GiHaLeMaSa00,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Giusti, Marc and H{\"a}gele, Klemens and Lecerf, Gr{\'e}goire and Marchand, Jo{\"e}l and Salvy, Bruno},
Date-Modified = {2006-03-14 10:24:40 +0100},
Doi = {10.1006/jsco.2000.0369},
Journal = {Journal of Symbolic Computation},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GiHaLeMaSa00.pdf},
Month = sep,
Number = 3,
Pages = {291--307},
Title = {Computing the Dimension of a Projective Variety: the Projective {N}oether {M}aple Package},
Volume = 30,
Year = 2000,
Abstract = {Recent theoretical advances in elimination theory use straight-line programs as a data structure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation of the dimension of a projective variety. Comparative results on benchmarks for time and space of several families of multivariate polynomial equation systems are given and we point out both weaknesses and advantages of different approaches. },
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.2000.0369}}
@article{SaSh99,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno and Shackell, John},
Date-Modified = {2006-03-14 10:24:49 +0100},
Doi = {10.1006/jsco.1999.0281},
Journal = {Journal of Symbolic Computation},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/SaSh99.pdf},
Month = jun,
Number = 6,
Pages = {543--563},
Title = {Symbolic Asymptotics: Multiseries of Inverse Functions},
Volume = 27,
Year = 1999,
Abstract = {We give an algorithm to compute an asymptotic expansion of multiseries type for the inverse of any given exp-log function. An example of the use of this algorithm to compute asymptotic expansions in combinatorics via the saddle-point method is then treated in detail. },
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1999.0281}}
@inproceedings{NicodemeSalvyFlajolet1999,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Nicod{\`e}me, Pierre and Salvy, Bruno and Flajolet, Philippe},
Booktitle = {Algorithms -- ESA'99},
Date-Added = {2005-07-24 18:10:25 +0800},
Date-Modified = {2009-10-05 09:15:59 +0200},
Doi = {10.1007/3-540-48481-7_18},
Editor = {Nesetril, Jaroslav},
Note = {Proceedings 7th Annual European Symposium on Algorithms, Prague, July~99. An extended version appeared in~\cite{NicodemeSalvyFlajolet02}.},
Number = 1643,
Pages = {194--211},
Series = {Lecture Notes in Computer Science},
Title = {Motif Statistics},
Url = {http://www.springerlink.com/link.asp?id=kn33ur4g65qcgyhg},
Year = 1999,
Abstract = {We present a complete analysis of the statistics of number of
occurrences of a regular expression
pattern in a random text. This covers ``motifs'' widely
used in computational biology.
Our approach is based on: {\em (i)\/} a constructive approach
to classical results in
theoretical computer science (automata and formal language theory),
in particular, the rationality of generating functions of regular
languages; {\em (ii)\/} analytic combinatorics that is used
for deriving
asymptotic properties from generating functions;
{\em (iii)\/}~computer algebra for determining generating functions
explicitly, analysing generating functions
and extracting coefficients efficiently. We provide
constructions for
overlapping or non-overlapping matches of a regular expression.
A companion
implementation produces multivariate generating functions for the statistics
under study. A fast computation of Taylor
coefficients of the generating functions then yields exact values of the
moments with typical application to random
texts of size 30,000 while
precise symptotic formul\ae\ allow predictions in texts
of arbitrarily large sizes. Our implementation was tested by
comparing predictions of the number of occurrences of motifs against
the 7~megabytes amino acid database {\sc Prodom}.
% consensus.
We handled more than $88\%$ of the standard collection of {\sc Prosite} motifs
with our programs.
Such comparisons help detect which motifs are observed in real
biological data more or less frequently than theoretically predicted.
},
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Bdsk-Url-1 = {http://www.springerlink.com/link.asp?id=kn33ur4g65qcgyhg},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/3-540-48481-7_18}}
@article{SaSh98,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno and Shackell, John},
Date-Added = {2005-07-24 18:09:38 +0800},
Date-Modified = {2006-03-14 10:24:57 +0100},
Doi = {10.1006/jsco.1997.0179},
Journal = {Journal of Symbolic Computation},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/SaSh98.pdf},
Month = mar,
Number = 3,
Pages = {329--349},
Title = {Symbolic Asymptotics: Functions of Two Variables, Implicit Functions},
Volume = 25,
Year = 1998,
Abstract = {A number of recent papers have been concerned with algorithms to decide the limiting behaviour of functions of a single variable. Here we make a corresponding study of a class of functions of two variables, namely the exp-log functions. As in the one-variable case, we need to make certain assumptions regarding the handling of constants.
Two of the main tools in the one-variable case are Hardy fields and nested forms. Here, we show how to compute some asymptotic estimates for two-variable exp-log functions. This method is then used to give an algorithm for computing the nested forms of real implicit functions.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1997.0179}}
@article{FlSa98,
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Added = {2005-07-24 18:08:31 +0800},
Date-Modified = {2006-01-21 12:41:40 +0100},
Journal = {Experimental Mathematics},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlSa98.pdf},
Number = 1,
Pages = {15--35},
Title = {Euler Sums and Contour Integral Representations},
Url = {http://www.math.ethz.ch/EMIS/journals/EM/restricted/7/7.1/flajolet.ps},
Volume = 7,
Year = 1998,
Abstract = {This paper develops an approach to the
evaluation of Euler sums that involve harmonic numbers,
either linearly or nonlinearly.
We give explicit formul{\ae} for
several classes of Euler sums
in terms of Riemann zeta values.
The approach is based on simple contour integral representations
and residue computations.},
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Bdsk-Url-1 = {http://www.math.ethz.ch/EMIS/journals/EM/restricted/7/7.1/flajolet.ps}}
@article{FlSa97,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Modified = {2006-03-14 10:25:11 +0100},
Doi = {10.1145/274888.274890},
Journal = {SIGSAM Bulletin},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlSa97.pdf},
Month = dec,
Number = 4,
Pages = {36--47},
Title = {The {S}IGSAM Challenges: Symbolic Asymptotics in Practice},
Volume = 31,
Year = 1997,
Abstract = {We present answers to 5 out of 10 of the ``Problems, Puzzles, Challenges'' proposed by G. J. Fee and M. B. Monagan in the March 1997 issue of the Sigsam Bulletin. In all cases, the answer to a seemingly numerical problem is obtained via series expansions and asymptotic methods. This illustrates more generally the crucial role played in the presence of singular behaviours by symbolic asymptotics as a bridge between symbolic computation and numerical computations. All our computations have been performed using MapleV.4 on a Dec Alpha (255/233). The timings indicated correspond to executions on this machine.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/274888.274890}}
@article{HaSa97,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Habsieger, Laurent and Salvy, Bruno},
Date-Modified = {2006-01-21 12:16:11 +0100},
Doi = {10.1090/S0025-5718-97-00829-6},
Journal = mc,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/HaSa97.pdf},
Month = apr,
Number = 218,
Owner = {bs},
Pages = {763--770},
Title = {On Integer {C}hebyshev Polynomials},
Url = {http://www.ams.org/mcom/1997-66-218/S0025-5718-97-00829-6/S0025-5718-97-00829-6.pdf},
Volume = 66,
Year = 1997,
Abstract = {We are concerned with the problem of minimizing the supremum norm
on [0,1] of a nonzero polynomial of degree at most
$n$ with integer coefficients. We use the structure of such polynomials
to derive an efficient algorithm for computing them. We give a table
of these polynomials for degree up to $75$ and use a value from this table
to answer an open problem and improve a lower bound due to Borwein and Erdelyi (1995).},
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Bdsk-Url-1 = {http://www.ams.org/mcom/1997-66-218/S0025-5718-97-00829-6/S0025-5718-97-00829-6.pdf},
Bdsk-Url-2 = {http://dx.doi.org/10.1090/S0025-5718-97-00829-6}}
@inproceedings{RiSaShVH96,
Address = {New York},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Richardson, Dan and Salvy, Bruno and Shackell, John and Van der Hoeven, Joris},
Booktitle = {Symbolic and Algebraic Computation},
Date-Modified = {2006-03-14 10:25:19 +0100},
Doi = {10.1145/236869.237089},
Editor = {Lakshman, Y. N.},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/RiSaShVH96.pdf},
Note = {Proceedings ISSAC'96, Z{\"u}rich, July 1996},
Pages = {309--313},
Publisher = {ACM Press},
Title = {Asymptotic Expansions of exp-log Functions},
Year = 1996,
Abstract = {We give an algorithm to compute
asymptotic expansions of exp-log functions. This
algorithm automatically computes the necessary
asymptotic scale and does not suffer from problems
of indefinite cancellation. In particular, an asymptotic
equivalent
can always be computed for a
given exp-log function.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/236869.237089}}
@article{GoSa96,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Gourdon, Xavier and Salvy, Bruno},
Date-Modified = {2006-03-14 10:25:25 +0100},
Doi = {10.1016/0012-365X(95)00133-H},
Journal = dm,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/GoSa96.pdf},
Number = {1--3},
Pages = {145--163},
Title = {Effective asymptotics of linear recurrences with rational coefficients},
Volume = 153,
Year = 1996,
Abstract = {We give algorithms to compute the asymptotic expansion of solutions of linear recurrences with rational coefficients and rational initial conditions in polynomial time in the order of the recurrence. },
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/0012-365X(95)00133-H}}
@article{SaSh95,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Shackell, John and Salvy, Bruno},
Date-Modified = {2006-03-14 10:25:37 +0100},
Doi = {10.1006/jsco.1995.1044},
Journal = jsc,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/SaSh95.pdf},
Number = 2,
Pages = {169--177},
Title = {Asymptotic Forms and Algebraic Differential Equations},
Volume = 20,
Year = 1995,
Abstract = {We analyse the complexity of a simple algorithm for computing asymptotic solutions of algebraic differential equations. This analysis is based on a computation of the number of possible asymptotic monomials of a certain order, and on the study of the growth of this number as the order of the equation grows.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1995.1044}}
@article{FlSa95,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Modified = {2006-03-14 10:25:44 +0100},
Doi = {10.1006/jsco.1995.1070},
Journal = jsc,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlSa95.pdf},
Number = {5-6},
Pages = {653--671},
Title = {Computer Algebra Libraries for Combinatorial Structures},
Volume = 20,
Year = 1995,
Abstract = {This paper introduces the framework of decomposable combinatorial structures and their traversal algorithms. A combinatorial type is decomposable if it admits a specification in terms of unions, products, sequences, sets, and cycles, either in the labelled or in the unlabelled context. Many properties of decomposable structures are decidable. Generating function equations, counting sequences, and random generation algorithms can be compiled from specifications. Asymptotic properties can be determined automatically for a reasonably large subclass. Maple libraries that implement such decision procedures are briefly surveyed (LUO, combstruct, equivalent). In addition, libraries for manipulating holonomic sequences and functions are presented (gfun, Mgfun).},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1995.1070}}
@article{LipshitzScottSalvy1995,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Lipshitz, Stanley P. and Scott, Tony C. and Salvy, Bruno},
Date-Modified = {2009-10-05 09:18:11 +0200},
Journal = {Journal of the Audio Engineering Society},
Month = {July/August},
Number = {7/8},
Owner = {bs},
Pages = {573--580},
Title = {On the Acoustic Impedance of Baffled Strip Radiators},
Volume = 43,
Year = 1995,
Abstract = {There appears to be no available expression for the reactive (mass) term in the acoustic
impedance of long baffled strip radiators, and the literature contains contradictory graphical data on both the real and the imaginary parts. Reliable data are important for the
proper electroacoustic design of ribbon transducers, and also potentially for other long,
narrow, low-mass planar radiators, both electrostatic and electrqmagnetic. Analytical
expressions and graphical data are presented for the resistive and reactive parts of the
acoustic load on an infinite baffled strip radiator.
},
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@article{FlLaLaSa95,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Labelle, Gilbert and Laforest, Louise and Salvy, Bruno},
Date-Modified = {2006-01-21 12:19:39 +0100},
Doi = {10.1002/rsa.3240070203},
Journal = RSA,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlLaLaSa95.pdf},
Number = 2,
Pages = {117--144},
Title = {Hypergeometrics and the cost structure of quadtrees},
Volume = 7,
Year = 1995,
Abstract = {Several characteristic parameters of randomly grown quadtrees of any dimension
are analysed.
Additive parameters have expectations whose
generating functions are expressible
in terms of generalized hypergeometric functions.
A complex asymptotic process based on
singularity analysis and integral representations
akin to Mellin transforms
leads to explicit values for various
structure constants related to path length,
retrieval costs, and storage occupation.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.3240070203}}
@book{GoSaZi95,
Author = {Gomez, Claude and Salvy, Bruno and Zimmermann, Paul},
Date-Modified = {2006-01-21 12:39:58 +0100},
Note = {ISBN 2-225-84780-0. 328 pages},
Publisher = {Masson},
Title = {Calcul formel : mode d'emploi. {E}xemples en {M}aple},
Year = 1995}
@article{DuSa95,
Author = {Dumas, Philippe and Salvy, Bruno},
Journal = mt,
Number = 2,
Owner = {bs},
Pages = {63--68},
Title = {Maple and the {P}utnam Competition},
Volume = 2,
Year = 1995}
@techreport{SaSl95,
Author = {Salvy, Bruno and Slavyanov, Sergey Yu.},
Date-Modified = {2006-01-21 12:39:45 +0100},
Institution = INRIA,
Number = 2600,
Title = {A Combinatorial Problem in the Classification of Second-Order Linear ODE's},
Type = {Research Report},
Url = {http://www.inria.fr/rrrt/rr-2600.html},
Year = 1995,
Abstract = {We study a problem of classification of linear homogeneous second-order ODE's
with polynomial coefficients based on qualitative properties of
singularities.
The corresponding combinatorial problem of counting the number of
classes is then solved in terms of the initial number of singularities.},
Bdsk-Url-1 = {http://www.inria.fr/rrrt/rr-2600.html}}
@article{Salvy94,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno},
Date-Modified = {2006-03-14 10:25:51 +0100},
Doi = {10.1006/jsco.1994.1014},
Journal = jsc,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/Salvy94.pdf},
Number = 3,
Owner = {bs},
Pages = {227--236},
Title = {Fast Computation of Some Asymptotic Functional Inverses},
Volume = 17,
Year = 1994,
Abstract = {G.~Robin showed that in several naturally occurring
asymptotic expansions of the form
\[y(x)\approx\sum_{n\ge0}{P_n(\log\log x)\over\log^n\!x},\]
the polynomials~$P_n$ satisfy a simple relation
\[P'_{n+1}=aP'_n+(bn+c)P_n.\]
These results do not give a way to compute these polynomials, since
the constant term remains undetermined by this equation. In this note,
we give a new derivation of some of Robin's results, and show how the
constant terms can be computed with only manipulations of one-variable
formal power series. From there, all the~$P_n$ can be computed
efficiently.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/jsco.1994.1014}}
@article{SaZi94,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno and Zimmermann, Paul},
Date-Modified = {2006-03-14 10:25:57 +0100},
Doi = {10.1145/178365.178368},
Journal = toms,
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/SaZi94.pdf},
Number = 2,
Owner = {bs},
Pages = {163--177},
Title = {Gfun: a {M}aple package for the manipulation of generating and holonomic functions in one variable},
Volume = 20,
Year = 1994,
Abstract = {We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended both as an elementary introduction to the subject and as a reference manual for the package.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/178365.178368}}
@inproceedings{PeSa93,
Address = {New York},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Petkov{\v s}ek, Marko and Salvy, Bruno},
Booktitle = {ISSAC'93},
Date-Modified = {2006-03-14 10:26:19 +0100},
Doi = {10.1145/164081.164087},
Editor = {Bronstein, Manuel},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/PeSa93.pdf},
Month = jul,
Pages = {27--33},
Publisher = {ACM Press},
Title = {Finding all hypergeometric solutions of linear differential equations},
Year = 1993,
Abstract = {Hypergeometric sequences are such that the quotient of two
successive terms is a fixed rational function of the index. We give a
generalization of
M.~Petkov{\v s}ek's algorithm to find all hypergeometric sequence
solutions of linear recurrences, and we
describe a program to find all hypergeometric functions that solve a linear
differential equation.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/164081.164087}}
@techreport{Salvy93b,
Author = {(editor), Bruno Salvy},
Date-Modified = {2006-01-21 12:02:15 +0100},
Institution = INRIA,
Month = dec,
Number = 2130,
Owner = {bs},
Title = {Algorithms Seminar, 1992--1993},
Type = {Research Report},
Url = {http://www.inria.fr/rrrt/rr-2130.html},
Year = 1993,
Abstract = {These seminar notes represent the proceedings (some in French) of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorial models and random generation, symbolic computati- on, asymptotic analysis, average-case analysis of algorithms and data structures and some computational number theory.},
Bdsk-Url-1 = {http://www.inria.fr/rrrt/rr-2130.html}}
@inproceedings{BrSa93,
Address = {New York},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bronstein, Manuel and Salvy, Bruno},
Booktitle = {ISSAC'93},
Date-Modified = {2006-03-14 10:26:09 +0100},
Doi = {10.1145/164081.164114},
Editor = {Bronstein, Manuel},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/BrSa93.pdf},
Month = jul,
Pages = {157--160},
Publisher = {ACM Press},
Title = {Full Partial Fraction Decomposition of Rational Functions},
Year = 1993,
Abstract = {We describe a rational algorithm that computes the full partial fraction
expansion of a rational function over the algebraic closure of its
field of definition. The algorithm uses only gcd operations over the initial
field but the resulting decomposition is expressed with linear denominators.
We give examples from its Axiom and Maple implementations.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/164081.164114}}
@article{Salvy93,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno},
Date-Modified = {2006-03-14 10:26:26 +0100},
Doi = {10.1145/165474.165477},
Journal = {SIGSAM Bulletin},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/Salvy93.pdf},
Month = apr,
Number = 2,
Pages = {1--12},
Title = {Efficient programming in {M}aple: a case study},
Volume = 27,
Year = 1993,
Abstract = {Studying the computation of orbits of some given group acting on a set, we show how successive refinements of a simple program provide a speedup factor of up to 200. The initial program cannot solve the problem at all, it is first converted into a program which needs one c.p.u. week and after all the optimizations have been performed, the computation takes only four hours. Although the problem is specific, we shall show that many of the optimizations we use are of interest for other problems as well.},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/165474.165477}}
@inproceedings{GourdonSalvy1993,
Author = {Gourdon, Xavier and Salvy, Bruno},
Booktitle = {Formal Power Series and Algebraic Combinatorics},
Date-Modified = {2009-10-26 17:48:57 +0100},
Editor = {Barlotti, A. and Delest, M. and Pinzani, R.},
Note = {Proceedings of FPSAC'5, Florence (Italy). An extended version appeared in Discrete Mathematics, 1996.},
Owner = {bs},
Pages = {253--266},
Title = {Asymptotics of linear recurrences with rational coefficients},
Year = 1993,
Abstract = {We give algorithms to compute the asymptotic expansion of solutions
of linear recurrences with rational coefficients and initial
conditions in polynomial time in the order of the recurrence.
}}
@article{FlSa93,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Salvy, Bruno},
Date-Modified = {2006-01-21 12:25:25 +0100},
Doi = {10.1137/1035147},
Journal = {SIAM Review},
Keywords = {holonomic functions},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlSa93.pdf},
Note = {Solution to Problem 92--18 by C. C. Grosjean},
Number = 4,
Pages = {645--646},
Title = {A Finite Sum of Products of Binomial Coefficients},
Url = {http://locus.siam.org/fulltext/SIREV/volume-35/1035147.pdf},
Volume = 35,
Year = 1993,
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Bdsk-Url-1 = {http://locus.siam.org/fulltext/SIREV/volume-35/1035147.pdf},
Bdsk-Url-2 = {http://dx.doi.org/10.1137/1035147}}
@article{GourdonSalvy1993a,
Author = {Gourdon, Xavier and Salvy, Bruno},
Date-Modified = {2009-10-26 17:45:21 +0100},
Journal = {The Maple Technical Newsletter},
Pages = {66--71},
Title = {Computing one million digits of $\sqrt{2}$},
Volume = {10},
Year = {1993},
Abstract = {We describe how the knowledge of Maple's internal data structure can
be used to compute the first million digits of $\sqrt{2}$ efficiently.
}}
@article{FlGoSa93,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Gourdon, Xavier and Salvy, Bruno},
Date-Modified = {2006-01-21 12:08:44 +0100},
Journal = {Gazette des Math{\'e}maticiens},
Keywords = {polynomials, special functions, asymptotics, zeros},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/FlGoSa93.pdf},
Month = jan,
Pages = {67--78},
Title = {Sur une famille de polyn{\^o}mes issus de l'analyse num{\'e}rique},
Volume = 55,
Year = 1993,
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@inproceedings{SaSh92,
Address = {New York},
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, Bruno and Shackell, John},
Booktitle = {Symbolic and Algebraic Computation},
Date-Modified = {2006-03-14 10:26:32 +0100},
Doi = {10.1145/143242.143292},
Editor = {Wang, Paul S.},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/SaSh92.pdf},
Note = {Proceedings of ISSAC'92, Berkeley, July 1992.},
Pages = {130--137},
Publisher = {ACM Press},
Title = {Asymptotic expansions of functional inverses},
Year = 1992,
Abstract = {We study the automatic computation of asymptotic expansions of
functional inverses. Based on previous work on asymptotic expansions,
we give an algorithm which computes Hardy-field solutions of
equations~$f(y)=x$, with~$f$ belonging to a large class of functions.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/143242.143292}}
@inproceedings{Salvy1992,
Author = {Salvy, Bruno},
Booktitle = {Asymptotic and Numerical Methods for Partial Differential Equations, Critical Parameters and Domain Decomposition},
Date-Modified = {2009-10-26 17:50:46 +0100},
Editor = {Kaper, H. and Garbey, M.},
Note = {Proceedings of a NATO Advanced Research Workshop, Beaune, France, May 1992.},
Publisher = {Kluwer Academic Publishers},
Title = {General Asymptotic Scales and Computer Algebra},
Year = 1992,
Abstract = {In many natural applications, one encounters asymptotic expansions of
a form more complicated than mere Puiseux series. Existing computer algebra systems lack
good algorithms for handling such asymptotic expansions. We present
tools that permit the representation and automatic handling of general
exp-log asymptotic expansions.
}}
@inproceedings{BergeronFlajoletSalvy1992,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Bergeron, Fran{\c c}ois and Flajolet, Philippe and Salvy, Bruno},
Booktitle = {CAAP'92},
Date-Modified = {2009-10-05 09:20:25 +0200},
Doi = {10.1007/3-540-55251-0_2},
Editor = {Raoult, J.-C.},
Note = {Proceedings of the 17th Colloquium on Trees in Algebra and Programming, Rennes, France, February 1992.},
Pages = {24--48},
Series = LNCS,
Title = {Varieties of Increasing Trees},
Volume = 581,
Year = 1992,
Abstract = {An increasing tree is a labelled rooted tree in which labels along
any branch from the root go in increasing order.
Under various guises,
such trees have surfaced as tree representations of permutations,
as data structures in computer science, and as probabilistic models
in diverse applications.
We present a unified generating function approach to the
enumeration of parameters on such trees.
The counting generating functions for several basic
parameters are shown to be related to a simple
ordinary differential equation
$$
{d\over dz}Y(z)=\phi(Y(z)),$$
which is non linear and autonomous.
Singularity analysis applied to the intervening generating functions
then permits to analyze asymptotically
a number of parameters of the trees,
like: root degree, number of leaves, path length, and level of nodes.
In this way it is found that various models share common features:
path length is $O(n\log n)$, the distributions of node levels and
number of leaves are asymptotically normal, etc.
},
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@article{FlajoletSalvyZimmermann1991,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Flajolet, Philippe and Salvy, Bruno and Zimmermann, Paul},
Date-Modified = {2009-10-26 17:55:43 +0100},
Doi = {10.1016/0304-3975(91)90145-R},
Journal = TCSA,
Month = feb,
Number = 1,
Pages = {37--109},
Title = {Automatic Average-case Analysis of Algorithms},
Volume = 79,
Year = 1991,
Abstract = {Many probabilistic properties of elementary discrete combinatorial structures of interest for the average-case analysis of algorithms prove to be decidable. This paper presents a general framework in which such decision procedures can be developed. It is based on a combination of generating function techniques for counting, and complex analysis techniques for asymptotic estimations.
We expose here the theory of exact analysis in terms of generating functions for four different domains: the iterative/recursive and unlabelled/labelled data type domains. We then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed.
A fair fragment of this theory is also incorporated into a system called Lambda-Upsilon-Omega. In this way, using computer algebra, one can produce automatically non-trivial average-case analyses of algorithms operating over a variety of ``decomposable'' combinatorial structures.
At a fundamental level, this paper is part of a global attempt at understanding why so many elementary combinatorial problems tend to have elementary asymptotic solutions. In several cases, it proves possible to relate entire classes of elementary combinatorial problems whose structure is well defined with classes of elementary ``special'' functions and classes of asymptotic forms relative to counting, probabilities, or average-case complexity.
},
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@article{Salvy91c,
Author = {Salvy, Bruno},
Date-Modified = {2006-01-21 12:30:56 +0100},
Journal = {The Maple Technical Newsletter},
Owner = {bs},
Pages = {32--42},
Title = {Three ways to get {S}tirling's formula in {M}aple},
Volume = 5,
Year = 1991}
@article{Salvy91b,
Askreprint = {Bruno.Salvy@inria.fr},
Author = {Salvy, B.},
Date-Modified = {2006-03-14 10:26:45 +0100},
Doi = {10.1145/122520.122521},
Journal = {SIGSAM Bulletin},
Local-Url = {file://localhost/Users/salvy/Biblio/Papers/Salvy91b.pdf},
Month = apr,
Number = 2,
Pages = {4--17},
Title = {Examples of automatic asymptotic expansions},
Volume = 25,
Year = 1991,
Abstract = {We describe the current state of a Maple library, gdev, designed to
perform asymptotic expansions for a large class of expressions. Many
examples are provided, along with a short sketch of the underlying
principles. At the time when this report is written, a striking feature of
these examples is that none of them can be computed directly with any
of today's most widespread symbolic computation systems
(Macsyma (Sun Release 309.6), Mathematica (Version 1.2,
beta test), Maple (Version 4.3) or Scratchpad~II (Version 4J)).
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/122520.122521}}
@phdthesis{Salvy1991b,
Author = {Salvy, Bruno},
Date-Modified = {2009-10-26 17:58:20 +0100},
Keywords = {asymptotic analysis, automatic asymptotics, computer algebra},
School = {{\'E}cole polytechnique},
Title = {Asymptotique automatique et fonctions g{\'e}n{\'e}ratrices},
Type = {Th{\`e}se de Doctorat},
Year = {1991},
Abstract = {The purpose of this thesis is to partially
automate asymptotic analysis. We first describe the mathematical
objects that underlie asymptotic expansions, and then introduce the
data structures and algorithms that correspond to them. With these
tools, the second chapter shows the automation of the asymptotic
expansion of integrals, for a wide class of integrands. The second
part of this thesis is devoted to the analysis of integral variables.
We recall the main properties of generating functions, and present in
detail the automatic extraction of asymptotic information about their
coefficients by purely syntactical operations. This constitutes the
analytical part of the~LUO system. This system, developed with
P.~Zimmermann, is capable of producing non-trivial average-case
analyses of algorithms and parameters of combinatorial structures. In
our last chapter, we describe its principles and scrutinize a variety
of examples to explain its use and working.}}
@techreport{FlajoletSalvyZimmermann1989a,
Author = {Flajolet, P. and Salvy, B. and Zimmermann, P.},
Date-Modified = {2009-10-26 18:03:01 +0100},
Institution = INRIA,
Month = aug,
Note = {116 pages},
Number = 1073,
Title = {{L}ambda-{U}psilon-{O}mega: {T}he 1989 {C}ookBook},
Type = {Research Report},
Url = {http://www.inria.fr/rrrt/rr-1073.html},
Year = {1989},
Abstract = {Lambda-Upsilon-Omega (LUO) is a research tool designed to assist the average case analysis of some well defined classes of algorithms and data structures. This cookbook consists of an informal introduction to the system together with eighteen examples of programmes that are automatically analyzed.
Amongst the applications treated here, we find: addition chains, quantitative concurrency analysis of simple systems, symbolic manipulation algorithms such as formal differentiation, simplification and rewriting systems, as well as combinatorial models including various tree and permutation statistics and functional graphs with applications to integer factorisation.
},
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Bdsk-Url-1 = {http://www.inria.fr/rrrt/rr-1073.html}}
@inproceedings{FlajoletSalvyZimmermann1989,
Author = {Flajolet, P. and Salvy, B. and Zimmermann, P.},
Booktitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting Codes},
Date-Modified = {2009-10-26 18:01:51 +0100},
Doi = {10.1007/3-540-51083-4_60},
Editor = {Mora, T.},
Note = {Proceedings AAECC'6, Rome, July 1988},
Pages = {201--212},
Series = LNCS,
Title = {{L}ambda-{U}psilon-{O}mega: An Assistant Algorithms Analyzer},
Volume = 357,
Year = 1989,
Abstract = {Lambda-Upsilon-Omega, LUO, is a system designed to perform automatic analysis of well-defined classes of algorithms operating over decomposable data structures.
It consists of an Algebraic Analyzer System that compiles algorithms specifications into generating functions of average costs, and an Analytic Analyzer System that extracts asymptotic informations on coefficients of generating functions. The algebraic part relies on recent methodologies in combinatorial analysis based on systematic correspondences between structural type definitions and counting generating functions. The analytic part makes use of partly classical and partly new correspondences between singularities of analytic functions and the growth of their Taylor coefficients.
The current version LUO0 of LUO implements as basic data types, term trees as encountered in symbolic algebra systems. The analytic analyzer can treat large classes of functions with explicit expressions. In this way, LUO0 can generate in the current stage about a dozen non-trivial average case analyses of algorithms like: formal differentiation, some algebraic simplification and matching algorithms. Its analytic analyzer can determine asymptotic expansions for large classes of generating functions arising in the analysis of algorithms.
The outline of a design for a full system is also discussed here. The long term goal is to include a fairly rich set of data structuring mechanisms including some general recursive type definitions, and have the analytic analyzer treat wide classes of functional equations as may be encountered in combinatorial analysis and the analysis of algorithms.
},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-51083-4_60}}
@techreport{Salvy88,
Author = {Salvy, B.},
Date-Modified = {2006-01-21 12:35:29 +0100},
Institution = {Universit{\'e} Paris XI},
Note = {Also available as INRIA Research Report 967 (1989)},
Title = {Fonctions g{\'e}n{\'e}ratrices et asymptotique automatique},
Type = {Rapport de {DEA}},
Url = {http://www.inria.fr/rrrt/rr-0967.html},
Year = {1988},
Bdsk-Url-1 = {http://www.inria.fr/rrrt/rr-0967.html}}
@string{INRIA = "Institut National de Recherche en Informatique et en Automatique"}
@proceedings{Salvy99,
Date-Added = {2006-01-21 11:59:10 +0100},
Date-Modified = {2006-03-31 09:48:51 +0200},
Editor = {Bruno Salvy},
Month = sep,
Organization = {Institut National de Recherche en Informatique et en Automatique},
Series = {Research Report},
Title = {Algorithms Seminar, 1998--1999},
Url = {http://www.inria.fr/rrrt/rr-3830.html},
Volume = {3830},
Year = 1999,
Abstract = {These seminar notes represent the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorics, symbolic computation, asymptotic analysis and average-case analysis of algorithms and data structures.
}}
@proceedings{Salvy98,
Date-Added = {2006-01-21 12:05:47 +0100},
Date-Modified = {2006-03-31 09:52:52 +0200},
Editor = {Bruno Salvy},
Month = sep,
Organization = {Institut National de Recherche en Informatique et en Automatique},
Series = {Research Report},
Title = {Algorithms Seminar, 1997--1998},
Url = {http://www.inria.fr/rrrt/rr-3504.html},
Volume = {3504},
Year = 1998,
Abstract = {These seminar notes represent the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorics, symbolic computation, asymptotic analysis and average-case analysis of algorithms and data structures.
}}
@proceedings{Salvy97,
Date-Modified = {2006-03-31 09:53:42 +0200},
Editor = {Bruno Salvy},
Month = sep,
Organization = {Institut National de Recherche en Informatique et en Automatique},
Series = {Research Report},
Title = {Algorithms Seminar, 1996--1997},
Url = {http://www.inria.fr/rrrt/rr-3267.html},
Volume = {3267},
Year = 1997,
Abstract = {These seminar notes represent the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorics, symbolic computation, asymptotic analysis and average-case analysis of algorithms and data structures.
}}
@proceedings{Salvy96,
Date-Modified = {2006-03-31 09:54:38 +0200},
Editor = {Bruno Salvy},
Month = sep,
Organization = {Institut National de Recherche en Informatique et en Automatique},
Series = {Research Report},
Title = {Algorithms Seminar, 1995--1996},
Url = {http://www.inria.fr/rrrt/rr-2992.html},
Volume = {2992},
Year = 1996}
@proceedings{Salvy95,
Date-Modified = {2006-03-31 09:55:46 +0200},
Editor = {Bruno Salvy},
Month = oct,
Organization = INRIA,
Series = {Research Report},
Title = {Algorithms Seminar, 1994--1995},
Url = {http://www.inria.fr/rrrt/rr-2669.html},
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Year = 1995,
Abstract = {These seminar notes represent the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorial models and random generation, symbolic computation, asymptotic analysis, average-case analysis of algorithms and data structures, and computational number theory.}}
@proceedings{Salvy94b,
Date-Added = {2006-01-21 12:03:28 +0100},
Date-Modified = {2006-03-31 09:56:47 +0200},
Editor = {Bruno Salvy},
Month = oct,
Organization = INRIA,
Series = {Research Report},
Title = {Algorithms Seminar, 1993--1994},
Url = {http://www.inria.fr/rrrt/rr-2381.html},
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Abstract = {These seminar notes represent the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorial models and random generation, symbolic computation, asymptotic analysis, average-case analysis of algorithms and data structures, and computational number theory.}}
@article{SalvyShackell2010,
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Author = {Salvy, Bruno and Shackell, John},
Date-Added = {2010-10-18 09:06:45 +0200},
Date-Modified = {2010-11-29 09:06:55 +0200},
Doi = {10.1112/jlms/jdq057},
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