Fix-Euler-Mahonian statistics on wreath products

Abstract

In 1997 Clarke et al. studied a $q$-analogue of Euler's difference table for $n!$ using a key bijection $\Psi$ on symmetric groups. In this paper we extend their results to the wreath product of a cyclic group with the symmetric group. In particular we obtain a new mahonian statistic \emph{fmaf} on wreath products. We also show that Foata and Han's two recent transformations on the symmetric groups provide indeed a factorization of $\Psi$.

20 pages, to appear in Advances in Applied Mathematics. Keywords: Derangements, Fix-Euler-Mahonian statistics, q-analogue, wreath product

References in corpus (1)

• Eulerian quasisymmetric functions and poset topology

Cited by in corpus (1)

• Higher Order Log-Concavity in Euler's Difference Table