6533b7d2fe1ef96bd125ed68

RESEARCH PRODUCT

The equidistribution of some Mahonian statistics over permutations avoiding a pattern of length three

Phan Thuan DoThi Thu Huong TranVincent Vajnovszki

subject

CombinatoricsDiscrete mathematicsFOS: Computer and information sciencesDiscrete Mathematics (cs.DM)StatisticsFOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - CombinatoricsCombinatorics (math.CO)Theoretical Computer ScienceMathematicsComputer Science - Discrete Mathematics

description

Abstract We prove the equidistribution of several multistatistics over some classes of permutations avoiding a 3-length pattern. We deduce the equidistribution, on the one hand of inv and foz e ″ statistics, and on the other hand that of maj and makl statistics, over these classes of pattern avoiding permutations. Here inv and maj are the celebrated Mahonian statistics, foz e ″ is one of the statistics defined in terms of generalized patterns in the 2000 pioneering paper of Babson and Steingrimsson, and makl is one of the statistics defined by Clarke, Steingrimsson and Zeng in (1997) [5] . These results solve several conjectures posed by Amini in (2018) [1] .

yearjournalcountryeditionlanguage
2022-02-01
http://arxiv.org/abs/2103.10357