Combinatorics of generalized q-Euler numbers

Authors:
Tim Huber;Ae Ja Yee
Affiliations:
Department of Mathematics, University of Texas--Pan American, Edinburg, TX, United States;Pennsylvania State University, Department of Mathematics, University Park, PA, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

Citing 5
Cited 1

Combinatorial Statistics on Alternating Permutations

Journal of Algebraic Combinatorics: An International Journal
Alternating permutations and symmetric functions

Journal of Combinatorial Theory Series A
Ramanujan's Lost Notebook: Part I

Ramanujan's Lost Notebook: Part I
Hadamard products for generalized Rogers--Ramanujan series

Journal of Approximation Theory
Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1

Zeros of generalized Rogers-Ramanujan series: Asymptotic and combinatorial properties

Journal of Approximation Theory

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Abstract

New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan's Lost Notebook. The results presented here are, in part, a response to a conjecture made by M.E.H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of the Rogers-Ramanujan series. Related generating functions appear in the work of H. Prodinger and L.L. Cristea in their study of geometrically distributed random variables. An elementary combinatorial interpretation for each of these enumerating functions is given in terms of a related set of statistics.