6 citations · 7 across the 5 of their papers we have counts for
6 papers
Free quasi-symmetric functions, product actions and quantum field theory of partitions
Gerard Henry Edmond Duchamp, Jean-Gabriel Luque, Karol A. Penson +1
We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enu…
A product formula and combinatorial field theory
A. Horzela, P. Blasiak, G. H. E. Duchamp +2
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - e…
One-parameter groups and combinatorial physics
Gerard Duchamp, Karol A. Penson, Allan I. Solomon +2
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the i…
The Boson Normal Ordering Problem and Generalized Bell Numbers
P. Blasiak, K. A. Penson, A. I. Solomon
For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e. we provide exact and explici…
Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited
Karol A. Penson, Allan I. Solomon
We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling nu…
Extended Bell and Stirling numbers from hypergeometric exponentiation
J. -M. Sixdeniers, K. A. Penson, A. I. Solomon
Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirl…