A sextuple equidistribution arising in Pattern Avoidance

TL;DR

This paper establishes a bijection linking specific pattern-avoiding sequences and permutations, revealing a sextuple equidistribution of statistics, and explores applications including permutation class characterization.

Contribution

It introduces a novel bijection between 021-avoiding inversion sequences and (2413,4213)-avoiding permutations, leading to new equidistribution results and permutation class characterizations.

Findings

Proves a sextuple equidistribution involving double Eulerian statistics.

Constructs a bijection between pattern-avoiding sequences and permutations.

Characterizes permutation classes with descent polynomials matching separable permutations.

Abstract

We construct an intriguing bijection between $021$-avoiding inversion sequences and $(2413,4213)$-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length $4$ whose descent polynomial equals that of separable permutations.