Return to Philippe Flajolet's Home Page
Everybody knows about the
Erdös number
that measures your distance to Paul Erdös in terms of
the shortest chain of coauthors.
(For nonmathematicians P. Erdös was one of the greatest
mathematician of the [20th] century with about 1,500 published papers
and 500 different coauthors.)
Well, plagiarizing Doron
Zeilberger,
the inspired poet of modern combinatorial analysis,
I have tried to determine some of my other "numbers"...
My Flajolet number is 0. I thought I was the only person with
that peculiar feature till I discovered that
the Library of Congress catalogues
a paper of 1913 (No, it's not me :-)):
-
Observatoire de Lyon (France),
Observations equatoriales et meridiennes faites a l'Observatoire de Lyon,
par MM. Le Cadet, Lagrula, Guillaume, Merlin et Flajolet. Lyon, A. Rey;
[etc., etc.] 1912. 3 p.l., [3]-311 p., 1 l. 26 cm.
LC CALL NUMBER: QB4 .L984
SUBJECTS:
Astronomy--Observations.
OTHER NAMES:
Le Cadet, M. (Georges), b. 1864.
Lagrula, M. (Joanny Philippe), b. 1870, joint author.
Guillaume, M. (Joseph Noel), b. 1863.
Merlin, M. (Jean), 1876-1914, joint author.
Flajolet, M. (Philipp), joint author.
SERIES TITLES (Indexed under SERI option):
Annales de l'Universite de Lyon. Nouv. ser. I. Sciences, medecine. fasc.
If you wonder, this paper was in fact
coauthored by
my
grand-father
who was at the time an astronomer at the
Observatory
of Lyon.
I am extremely proud of my Knuth number
that is equal to 1 via the path:
-
Flajolet, Philippe; Knuth, Donald E.; Pittel, Boris The first cycles in an evolving graph.
Graph theory and combinatorics (Cambridge, 1988). Discrete Math. 75 (1989), no. 1-3, 167--215.
For multiple (and happy) reasons, my Odlyzko number is also 1.
-
Flajolet, P., Odlyzko, A.
The average height of binary trees and other simple
trees. J. Comput. System Sci. 25 (1982), no. 2, 171--213.
Consequently, my Erdös number is 2 (by way
of Odlyzko, but also Richmond), a property that I share in fact with more
than 5,000 scientists.
-
P. Erdos, A. Hildebrand, A. Odlyzko, P. Pudaite, and B. Reznick.
The asymptotic behavior of a family of sequences,
Pacific J. Math., 126 (1987), pp. 227-241.
- [Odlyzko->Flajolet]
My Wiles number is equal to 4 (Gee!) via the path:
-
J. Coates and A. Wiles, `On $p$-adic $L$-functions and elliptic units.' Australian Mathematical Society. Journal.
Series A, 26(1978), 1--25.
-
M.K. Agrawal, J.H. Coates, D.C. Hunt and A.J. van der Poorten, `Elliptic curves of conductor $11$', Mathematics
of Computation, 35(1980), 991--1002.
-
J. -P. Allouche, A. Lubiw, M. Mendes France, A. van der Poorten, and J. Shallit,`Convergents of folded continued
fractions', Acta Arithmetica, 77(1996), 77-96.
-
J.-P. Allouche, P. Flajolet, and M. Mendes France, `Algebraically independent formal power series: a language
theory interpretation.', Analytic number theory (Tokyo, 1988) Lecture Notes in Math., 1434, Springer, Berlin,;
11--18.
I am ashamed of my Zeilberger number that is only 3:
-
Wilf, H. S.; Zeilberger, D.
An algorithmic proof theory for hypergeometric
(ordinary and "$q$") multisum/integral identities.
Invent. Math. 108 (1992), no. 3, 575--633.
-
Knuth, D. E.; Wilf, H. S.
A short proof of Darboux's lemma. Appl. Math. Lett. 2
(1989), no. 2, 139--140.
-
Flajolet, Philippe; Knuth, Donald E.; Pittel, Boris The first cycles in an evolving graph.
Graph theory and combinatorics (Cambridge, 1988). Discrete Math. 75 (1989), no. 1-3, 167--215.
But, thanks to Doron
(Zeilberger), my Einstein number is as low as 6:
-
Einstein, A. and Kaufman, B., A new form of the general relativistic field equations. Ann. of Math. (2) 1955, 62,
128--138.
-
Gillis, J. Kaufman, B., The stability of a rotating viscous jet. Quart. Appl. Math. 1962, 19, 301--308.
-
Gillis, J. Zeilberger, D. A direct combinatorial proof of a positivity result. European Journal of Combinatorics,
1983, 4, no. 3, 221--223.
- [Zeilberger->Wilf->Knuth->Flajolet]