On (shape-)Wilf-equivalence for words

TL;DR

This paper extends a known permutation Wilf-equivalence result to the broader context of words, demonstrating that certain pattern-avoidance properties are preserved in this more general setting.

Contribution

The authors generalize a permutation Wilf-equivalence result to words, broadening the understanding of pattern avoidance in combinatorics.

Findings

Equivalence between avoiding 231γ and 312γ patterns extended to words

Demonstrates symmetry in pattern avoidance for words

Provides new insights into pattern-avoidance enumeration in combinatorics

Abstract

Stankova and West showed that for any non-negative integer $s$ and any permutation $\gamma$ of $\{4,5,\dots,s+3\}$ there are as many permutations that avoid $231\gamma$ as there are that avoid $312\gamma$. We extend this result to the setting of words.