6533b85efe1ef96bd12bfe97

RESEARCH PRODUCT

Mahonian STAT on rearrangement class of words

Ting HuaVincent VajnovszkiShishuo Fu

subject

FOS: Computer and information sciencesInvolution (mathematics)Mathematics::CombinatoricsDiscrete Mathematics (cs.DM)Applied Mathematics05A05 05A190211 other engineering and technologies021107 urban & regional planning0102 computer and information sciences02 engineering and technology01 natural sciencesRobinson–Schensted–Knuth correspondenceCombinatorics010201 computation theory & mathematicsFOS: MathematicsMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsCombinatorics (math.CO)AlphabetFixed lengthComputer Science - Discrete MathematicsMathematics

description

In 2000, Babson and Steingr\'{i}msson generalized the notion of permutation patterns to the so-called vincular patterns, and they showed that many Mahonian statistics can be expressed as sums of vincular pattern occurrence statistics. STAT is one of such Mahonian statistics discoverd by them. In 2016, Kitaev and the third author introduced a words analogue of STAT and proved a joint equidistribution result involving two sextuple statistics on the whole set of words with fixed length and alphabet. Moreover, their computer experiments hinted at a finer involution on $R(w)$, the rearrangement class of a given word $w$. We construct such an involution in this paper, which yields a comparable joint equidistribution between two sextuple statistics over $R(w)$. Our involution builds on Burstein's involution and Foata-Sch\"{u}tzenberger's involution that utilizes the celebrated RSK algorithm.

yearjournalcountryeditionlanguage
2017-08-26Discrete Applied Mathematics
https://doi.org/10.1016/j.dam.2019.06.010