Algorithmic coincidence classification of mesh patterns

TL;DR

This paper advances the classification of mesh pattern coincidences by introducing a force concept, completing the classification for patterns up to size three, and demonstrating its use in enumerating permutation classes.

Contribution

It introduces the notion of a force on permutation patterns and applies it to classify mesh pattern coincidences, extending previous results and enabling enumeration of classical permutation classes.

Findings

Completed the classification of mesh pattern coincidences up to size three.

Introduced the concept of a force on permutation patterns.

Showed how the force concept can be used to enumerate permutation classes.

Abstract

We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size three. We also show that this concept can be used to enumerate classical permutation classes.