KAIST Discrete Math Seminar

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.