Equidistributions of MAJ and STAT over pattern avoiding permutations
release_rc7akbswevay3llxs36vqfv5j4
by
Joanna N. Chen
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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