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

Andrew Beveridge; Kristin Heysse; Paige Robertson

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

Combinatorics 2026-07-20 v1

Authors: Andrew Beveridge , Kristin Heysse , Paige Robertson

Abstract

A permutation $\pi \in S_n$ is (32-1)-avoiding when there do not exist $1 \leq i < i+1 < j \leq n$ such that $\pi_i > \pi_{i+1} > \pi_j$ . 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.

Cite

@article{arxiv.2607.18417,
  title  = {(32-1)-Avoiding Permutations with Maximum Inversion Number},
  author = {Andrew Beveridge and Kristin Heysse and Paige Robertson},
  journal= {arXiv preprint arXiv:2607.18417},
  year   = {2026}
}

Comments

25 pages, 12 figures