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

2026/07/20 by Andrew Beveridge, Kristin Heysse, Paige Robertson · 1 citation
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Abstract

A permutation π∈ S_n is (32-1)-avoiding when there do not exist 1 ≤ i < i+1 < j ≤ 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.

Cited by

• Lehmer Codes and the Reverse-Complement Mapping from (32-1)-Avoiding Permutations to (3-21)-Avoiding Permutations

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