Equidistributions of MAJ and STAT over pattern avoiding permutations release_rc7akbswevay3llxs36vqfv5j4

by Joanna N. Chen

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2017  

Abstract

Babson and Steingrímsson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by the combination of generalized pattern functions. Particularly, they defined a new Mahonian statistic in terms of generalized pattern functions, which is denoted stat. Recently, Amini investigated the equidistributions of these Mahonian statistics over sets of pattern avoiding permutations. Moreover, he posed several conjectures. In this paper, we construct a bijection from S_n(213) to S_n(231), which maps the statistic (maj,stat) to the statistic (stat,maj). This allows us to give solutions to some of Amini's conjectures.
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Date   2017-07-22
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arXiv  1707.07195v1
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