Doubloons and q-secant numbers

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

1 Institut Lothaire
2 IRMA - Institut de Recherche Mathématique Avancée

Based on the evaluation at $t=-1$ of the generating polynomial for the hyperoctahedral group by the number of descents, an observation recently made by Hirzebruch, a new $q$-secant number is derived by working with the Chow-Gessel $q$-polynomial involving the flag major index. Using the doubloon combinatorial model we show that this new $q$-secant number is a polynomial with positive integral coefficients, a property apparently hard to prove by analytical methods.

Domaines: Combinatoire [math.CO]

Dominique Foata, Guo-Niu Han. Doubloons and q-secant numbers. Münster Journal of Mathematics, 2010, 3, pp.89-110. ⟨hal-00579808⟩