Inflations of Geometric Grid Classes: Three Case Studies

TL;DR

This paper investigates the enumeration of three permutation classes defined by two forbidden patterns of length four, using inflations of geometric grid classes to analyze their structure.

Contribution

It introduces a novel approach applying inflations of geometric grid classes to enumerate specific permutation classes with forbidden patterns.

Findings

Successful enumeration of three permutation classes

Development of techniques for inflations of geometric grid classes

Insights into the structure of pattern-avoiding permutations

Abstract

We enumerate three specific permutation classes defined by two forbidden patterns of length four. The techniques involve inflations of geometric grid classes.