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.