A combinatorial interpretation of the Seidel generation of qderangement numbers

Abstract. In [8] Dumont and Randrianarivony have given several combinatorial interpretations for the coefficients of the Euler-Seidel matrix associated to n!. In this paper we consider a q-analogue of their results, which leads to the discovery of a new mahonian statistic “maf ” on the symmetric group. We then give new proofs and generalizations of some results of Gessel and Reutenauer [12] and Wachs [17]