%0 Journal Article
%T Generalized Dumont-Foata polynomials and alternative tableaux
%A Matthieu Josuat-Verg¨¨s
%J Mathematics
%D 2010
%I arXiv
%X Dumont and Foata introduced in 1976 a three-variable symmetric refinement of Genocchi numbers, which satisfies a simple recurrence relation. A six-variable generalization with many similar properties was later considered by Dumont. They generalize a lot of known integer sequences, and their ordinary generating function can be expanded as a Jacobi continued fraction. We give here a new combinatorial interpretation of the six-variable polynomials in terms of the alternative tableaux introduced by Viennot. A powerful tool to enumerate alternative tableaux is the so-called "matrix Ansatz", and using this we show that our combinatorial interpretation naturally leads to a new proof of the continued fraction expansion.
%U http://arxiv.org/abs/1005.4007v2