School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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.
Recommended Citation
Huber, T., & Yee, A. J. (2010). Combinatorics of generalized q-Euler numbers. Journal of Combinatorial Theory, Series A, 117(4), 361–388. https://doi.org/10.1016/j.jcta.2009.07.012
Publication Title
Journal of Combinatorial Theory, Series A
DOI
10.1016/j.jcta.2009.07.012
Comments
© 2009 Elsevier Inc. All rights reserved.