Length-Four Pattern Avoidance in Inversion Sequences

TL;DR

This paper classifies pattern avoidance in inversion sequences of length four, identifying equivalence classes and enumerating sequences, thus advancing understanding of combinatorial structures related to permutations.

Contribution

It provides a complete classification of Wilf equivalence classes for length-4 pattern-avoiding inversion sequences, except for one unresolved case.

Findings

Classified all Wilf equivalence classes for length-4 patterns

Enumerated several pattern-avoiding inversion sequences in OEIS

Identified an open case regarding pattern equivalence

Abstract

Inversion sequences of length $n$ are integer sequences $e_1,\ldots ,e_n$ with $0\le e_i<i$ for all $i$, which are in bijection with the permutations of length $n$. In this paper, we classify all Wilf equivalence classes of pattern-avoiding inversion sequences of length-4 patterns except for one case (whether 3012 $\equiv$ 3201) and enumerate some of the length-4 pattern-avoiding inversion sequences that are in the OEIS.