Combinatorics of generalized q-Euler numbers

Ae Ja Yee (이애자)

Dept. of Mathematics, Pennsylvania State University, University Park, USA.

Dept. of Mathematics, Pennsylvania State University, University Park, USA.

2008/07/03 Thu, 4PM-5PM

The Euler number E_{n} counts the number of alternating permutations on the set [n]. It is well known that its exponential generating function equals Tan *z* + Sec *z*. For this reason, E_{2n} and E_{2n+1} are called *secant numbers* and *tangent numbers*, respectively. Certain polynomials arising in series expansions for zeros of generalized Rogers-Ramanujan functions provide a q-analog of the tangent numbers, which is part of a wider class of polynomials with similar combinatorial interpretations. In this talk, we will discuss various q-Euler numbers. This is a joint work with Tim Huber from Iowa State University.

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