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arXiv · 0810.2731

Fix-Euler-Mahonian statistics on wreath products

Hilarion L. M. Faliharimalala·Jiang Zeng
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Abstract

In 1997 Clarke et al. studied a $q$-analogue of Euler's difference table for $n!$ using a key bijection $Ψ$ 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 $Ψ$.

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Hilarion L. M. Faliharimalala, Jiang Zeng. 2009-12-01. Fix-Euler-Mahonian statistics on wreath products. https://arxiv.org/abs/0810.2731

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