December 3, 2007
10h30:
Some Combinatorial Problems Inherent in and Related to Quantum Statistics.
By
Karol A. Penson (LPTMC, Université de Paris VI)
Abstract.
We shall present a general view of combinatorial
aspects of the normal ordering of functions of Boson creation and
annihilation operators. It will be shown that this procedure naturally
leads to far reaching generalizations of classical combinatorial Bell
and Stirling numbers for which closed form analytic formulas in terms
of hypergeometric functions are obtained. These representations,
termed extended Dobinski-type relations, allow to consider all these
sequences as Stieltjes moments of probability distributions whose
explicit forms are obtained via inverse Mellin transform. Links with
the forthcoming presentations by Blasiak and by Duchamp will be
pointed out.
Contact Information Virginie Collette