Year: 2025
Type: article
Abstract: Let s be West's deterministic stack-sorting map.A well-known result is that every length n permutation is sorted with n -1 iterations of s.In 2020, Defant introduced the notion of highly-sorted permutationspermutations obtained by applying slightly less than n -1 iterations of s.In 2023, Choi & Choi extended this notion to generalized stack-sorting maps s σ , where we relax the condition of becoming sorted to the analogous condition of becoming periodic with respect to s σ .While periodicity seems counterintuitive in the context of sorting, it arises naturally in these restrictive forms, where the map is studied as an operator with properties rather than a means to "sort" permutations in the usual sense.In this work, we introduce the notion of minimally-sorted permutations as an antithesis to Defant's highlysorted permutations, and show that the order of the (123, 132)-avoiding stack-sorting map is 2 n-1 2 .
Author: Owen Zhang
Institution: Yale University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409744009