Describing West-3-stack-sortable permutations with permutation patterns

TL;DR

The paper introduces a novel method using mesh and decorated patterns to analyze permutations sorted by multiple stack passes, specifically focusing on West-3-stack-sortable permutations and applications to bubble-sort.

Contribution

It presents a new pattern-based approach for characterizing permutations sortable by multiple stack passes, expanding the understanding of permutation sorting complexity.

Findings

Characterization of West-3-stack-sortable permutations

Application of the method to bubble-sort operator

Introduction of decorated patterns for permutation analysis

Abstract

We describe a new method for finding patterns in permutations that produce a given pattern after the permutation has been passed once through a stack. We use this method to describe West-3-stack-sortable permutations, that is, permutations that are sorted by three passes through a stack. We also show how the method can be applied to the bubble-sort operator. The method requires the use of mesh patterns introduced by Br\"and\'en and Claesson (2011), as well as a new type of generalized pattern we call a decorated pattern.