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

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.