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arXiv · 1109.3353

Euler-Mahonian Statistics via Polyhedral Geometry

Matthias Beck·Benjamin Braun
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Abstract

A variety of descent and major-index statistics have been defined for symmetric groups, hyperoctahedral groups, and their generalizations. Typically associated to pairs of such statistics is an Euler--Mahonian distribution, a bivariate generating function identity encoding these statistics. We use techniques from polyhedral geometry to establish new multivariate generalizations for many of the known Euler--Mahonian distributions. The original bivariate distributions are then straightforward specializations of these multivariate identities. A consequence of these new techniques are bijective proofs of the equivalence of the bivariate distributions for various pairs of statistics.

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Matthias Beck, Benjamin Braun. 2013-05-21. Euler-Mahonian Statistics via Polyhedral Geometry. https://arxiv.org/abs/1109.3353

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