##### Proceedings of the American Mathematical Society, volume
138 (2010), no. 2, 385-393.

# Dominique Foata, Guo-Niu Han

#
THE q-TANGENT AND q-SECANT NUMBERS VIA BASIC EULERIAN
POLYNOMIALS

**Abstract.**
The classical identity that relates Eulerian polynomials to tangent
numbers together with the parallel result dealing with secant numbers
is given a q-extension, both analytically and combinatorially. The
analytic proof is based on a recent result by Shareshian and Wachs
and the combinatorial one on the geometry of alternating
permutations.

foata at math dot u-strasbg dot fr,
guoniu at math dot u-strasbg dot fr

The following version is available: