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

A permutation $\pi \in S_n$ is (32-1)-avoiding when there do not exist $1\le i<i+1<j\le n$ 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.