The q-tangent and q-secant numbers via basic Eulerian polynomials

Dominique Foata (1) , Guo-Niu Han (2)

1 Institut Lothaire
2 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Combinatoire [math.CO]

Dominique Foata, Guo-Niu Han. The q-tangent and q-secant numbers via basic Eulerian polynomials. Proc. Amer. Math. Soc., 2009, 138, pp.385-393. ⟨hal-00438479⟩