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arXiv · 2607.18417

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

Andrew Beveridge·Kristin Heysse·Paige Robertson
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Abstract

A permutation $π\in S_n$ is (32-1)-avoiding when there do not exist $1 \leq i < i+1 < j \leq n$ such that $π_i > π_{i+1} > π_j$. 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.

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Andrew Beveridge, Kristin Heysse, Paige Robertson. 2026-07-20. (32-1)-Avoiding Permutations with Maximum Inversion Number. https://arxiv.org/abs/2607.18417

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