On 0012-avoiding inversion sequences and a Conjecture of Lin and Ma

TL;DR

This paper confirms a conjecture by Lin and Ma on counting inversion sequences avoiding the pattern 0012, providing explicit formulas for their enumeration and those with specific last entries.

Contribution

The paper proves Lin and Ma's conjecture and derives formulas for counting 0012-avoiding inversion sequences, including those with last entry equal to n-1.

Findings

Confirmed the conjecture on 0012-avoiding inversion sequences.

Derived explicit enumeration formulas for these sequences.

Provided formulas for sequences with specific last entries.

Abstract

The study of pattern avoidance in inversion sequences recently attracts extensive research interests. In particular, Zhicong Lin and Jun Ma conjectured a formula that counts the number of inversion sequences avoiding the pattern $0012$. We will not only confirm this conjecture but also give a formula that enumerates the number of $0012$-avoiding inversion sequences in which the last entry equals $n-1$.