The Order of the (123, 132)-Avoiding Stack Sort

Let s be West's deterministic stack-sorting map. A well-known result (West) is that any length n permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations in sᵗ(Sₙ) for t n-1. In 2023, Choi and Choi extended this notion to generalized stack-sorting maps sσ, where we relax the condition of becoming sorted to the analogous condition of becoming periodic with respect to sσ. In this work, we introduce the notion of minimally-sorted permutations Mₙ as an antithesis to Defant's highly-sorted permutations, and show that ord_s123, 132(Sₙ) = 2 n-1/2 , strengthening Berlow's 2021 classification of periodic points.