Further equidistribution of set-valued statistics on permutations

TL;DR

This paper extends the understanding of permutation statistics by constructing bijections that demonstrate the equidistribution of certain set-valued statistics, broadening previous results to include sextuple set-valued cases.

Contribution

The authors develop bijections to prove the equidistribution of two pairs of sextuple set-valued permutation statistics, extending prior work on integer-valued and bivariable set-valued statistics.

Findings

Established equidistribution of two pairs of sextuple set-valued permutation statistics

Extended previous results to more complex set-valued statistics

Built bijections demonstrating these statistical symmetries

Abstract

We construct bijections to show that two pairs of sextuple set-valued statistics of permutations are equidistributed on symmetric groups. This extends a recent result of Sokal and the second author valid for integer-valued statistics as well as a previous result of Foata and Han for bivariable set-valued statistics.