Pattern Avoiding Permutations Enumerated by Inversions

TL;DR

This paper explores the enumeration of indecomposable permutations avoiding certain patterns of length up to 3, focusing on inversion-based enumeration rather than size, extending classical pattern avoidance studies.

Contribution

It provides a comprehensive analysis of pattern-avoiding permutations enumerated by inversions, specifically for patterns of length up to 3, highlighting new enumeration results.

Findings

Enumeration formulas for indecomposable pattern-avoiding permutations by inversions.

Complete classification of pattern combinations of length up to 3.

Extension of classical pattern avoidance results to inversion-based enumeration.

Abstract

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion and Schmidt, we investigate all combinations of permutation patterns of length at most 3.