Arithmetic properties of generalized Euler numbers

Details Arithmetic properties of generalized Euler numbers Arithmetic properties of generalized Euler numbers

1998-01-02

arxiv.org/abs/math/9801010v1

Southeast Asian Bull. Math. 21 (1997), 73-78

Mathematics

Combinatorics

9 pages, 0 figures, Latex, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

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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