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Arithmetic properties of generalized Euler numbers

Bruce E. Sagan·Ping Zhang
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Abstract

The generalized Euler number E_{n|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 E_{n|k}. In particular, we generalize two theorems of Andrews and Gessel about factors of the q-tangent numbers.

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Bruce E. Sagan, Ping Zhang. 1998-01-02. Arithmetic properties of generalized Euler numbers. https://arxiv.org/abs/math/9801010

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