(32-1)-Avoiding Permutations with Maximum Inversion Number

Andrew Beveridge; Kristin Heysse; Paige Robertson

paper

(32-1)-Avoiding Permutations with Maximum Inversion Number

arXiv:2607.18417

Abstract

A permutation $I ¨ \in S_{n}$ is (32-1)-avoiding when there do not exist $1 \leq i < i + 1 < j \leq n$ such that $I ¨ _{i} > I ¨ _{i + 1} > I ¨ _{j}$ . We determine the maximum inversion number for (32-1)-avoiding permutations and count the number of permutations that achieve this maximum. We then provide a direct construction that enumerates these permutations.

25 pages, 12 figures