Title

Combinatorics of generalized q-Euler numbers

Document Type

Article

Publication Date

5-2010

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.

Comments

© 2009 Elsevier Inc. All rights reserved.

Publication Title

Journal of Combinatorial Theory, Series A

DOI

10.1016/j.jcta.2009.07.012

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