Fix-Euler-Mahonian statistics on wreath products

Details Fix-Euler-Mahonian statistics on wreath products Fix-Euler-Mahonian statistics on wreath products

2008-10-15

arxiv.org/abs/0810.2731v3

Mathematics

Combinatorics

20 pages, to appear in Advances in Applied Mathematics

Scientific paper

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 $\Psi$.

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