Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.06177 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910441782902784 |
|---|---|
| author | Diaz-Lopez, Alexander Haymaker, Kathryn McGarry, Colin McMahon, Dylan |
| author_facet | Diaz-Lopez, Alexander Haymaker, Kathryn McGarry, Colin McMahon, Dylan |
| contents | Let $S_n$ be the symmetric group on the set $[n]:=\{1,2,\ldots,n\}$. Given a permutation $σ=σ_1σ_2 \cdots σ_n \in S_n$, we say it has a descent at index $i$ if $σ_i>σ_{i+1}$. Let $\mathcal{D}(σ)$ be the set of all descents of $σ$ and define $\mathcal{D}(S;n)=\{σ\in S_n\, | \,\mathcal{D}(σ)=S\}$. We study the Hamming metric and $\ell_\infty$-metric on the sets $\mathcal{D}(S;n)$ for all possible nonempty $S\subset[n-1]$ to determine the maximum possible value that these metrics can achieve when restricted to these subsets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metrics on permutations with the same descent set Diaz-Lopez, Alexander Haymaker, Kathryn McGarry, Colin McMahon, Dylan Combinatorics 05A05, 05A15 Let $S_n$ be the symmetric group on the set $[n]:=\{1,2,\ldots,n\}$. Given a permutation $σ=σ_1σ_2 \cdots σ_n \in S_n$, we say it has a descent at index $i$ if $σ_i>σ_{i+1}$. Let $\mathcal{D}(σ)$ be the set of all descents of $σ$ and define $\mathcal{D}(S;n)=\{σ\in S_n\, | \,\mathcal{D}(σ)=S\}$. We study the Hamming metric and $\ell_\infty$-metric on the sets $\mathcal{D}(S;n)$ for all possible nonempty $S\subset[n-1]$ to determine the maximum possible value that these metrics can achieve when restricted to these subsets. |
| title | Metrics on permutations with the same descent set |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2405.06177 |