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 s_, where we relax the condition of becoming sorted to the analogous condition of becoming periodic with respect to s_. In this work, we introduce the notion of minimally-sorted permutations Mₙ as an antithesis to Defant's highly-sorted permutations, and show that ordₒ_₁₂₃, ₁₃₂ (Sₙ) = 2 n-12, strengthening Berlow's 2021 classification of periodic points.