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
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