Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01854 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916233837805568 |
|---|---|
| author | Zhang, Owen |
| author_facet | Zhang, Owen |
| contents | 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 $s^t(S_n)$ for $t \lessapprox n-1.$ In 2023, Choi and 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 $s_σ.$ In this work, we introduce the notion of minimally-sorted permutations $\mathfrak{M}_n$ as an antithesis to Defant's highly-sorted permutations, and show that $\text{ord}_{s_{123, 132}}(S_n) = 2 \lfloor \frac{n-1}{2} \rfloor,$ strengthening Berlow's 2021 classification of periodic points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Order of the (123, 132)-Avoiding Stack Sort Zhang, Owen Combinatorics 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 $s^t(S_n)$ for $t \lessapprox n-1.$ In 2023, Choi and 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 $s_σ.$ In this work, we introduce the notion of minimally-sorted permutations $\mathfrak{M}_n$ as an antithesis to Defant's highly-sorted permutations, and show that $\text{ord}_{s_{123, 132}}(S_n) = 2 \lfloor \frac{n-1}{2} \rfloor,$ strengthening Berlow's 2021 classification of periodic points. |
| title | The Order of the (123, 132)-Avoiding Stack Sort |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.01854 |