Arithmetic properties of generalized Euler numbers
Abstract
The generalized Euler number En|k counts the number of permutations of 1,2,...,n which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k=2. In this paper, we study divisibility properties of a q-analog of En|k. In particular, we generalize two theorems of Andrews and Gessel about factors of the q-tangent numbers.
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