Equidistributions of MAJ and STAT over pattern avoiding permutations
arXiv:1707.07195
Abstract
Babson and Steingr\'ımsson 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 . 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 to , which maps the statistic to the statistic . This allows us to give solutions to some of Amini's conjectures.
10 pages