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arXiv · 1705.05298

Equidistributions of Mahonian statistics over pattern avoiding permutations

Nima Amini
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Abstract

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingrimsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over pattern avoiding sets of permutations. Tools used include block decomposition, Dyck paths and generating functions.

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Nima Amini. 2017-05-15. Equidistributions of Mahonian statistics over pattern avoiding permutations. https://arxiv.org/abs/1705.05298

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