Q-Polynômes de Gandhi et statistique de Denert

Abstract

Using the q-difference operator we give q-analogues of the Gandhi polynomials of the first and second kinds, which are extensions of the Genocchi and median Genocchi numbers, respectively. We provide two combinatorial interpretations of these polynomials in terms of generating functions for Genocchi permutations by some appropriate statistics, one of them being essentially the Denert statistic. We also derive the continued fraction expansions for their ordinary generating functions.