Metrics on Signed Permutations with the Same Peak Set
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911113699917824 |
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| author | Andrus, Kayla Larsen, Nathaniel MacLennan, Alyssa Kirby, Gordon Rojas Garcia, Mariana Smit Vega Vicars, Christian |
| author_facet | Andrus, Kayla Larsen, Nathaniel MacLennan, Alyssa Kirby, Gordon Rojas Garcia, Mariana Smit Vega Vicars, Christian |
| contents | Let $S^B_n$ be the Coxeter group of type B. We denote the set of indices where $σ\in S^B_n$ has a peak as $Peak(σ)$ and let $P^{B}(S;n)=\{σ\in S^{B}_n~|~ Peak(σ)=S\}$. In \cite{metrics}, Diaz-Lopez, Haymaker, Keough, Park and White considered metrics for unsigned permutations with the same peak set. In this paper, we generalize their result by studying Hamming, $l_{\infty}$, and the word metrics on $P^{B}(S;n)$ for all $S$. We also determine the minimum and maximum possible values that these metrics can achieve in these subsets of $S^B_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metrics on Signed Permutations with the Same Peak Set Andrus, Kayla Larsen, Nathaniel MacLennan, Alyssa Kirby, Gordon Rojas Garcia, Mariana Smit Vega Vicars, Christian Combinatorics 05A05 Let $S^B_n$ be the Coxeter group of type B. We denote the set of indices where $σ\in S^B_n$ has a peak as $Peak(σ)$ and let $P^{B}(S;n)=\{σ\in S^{B}_n~|~ Peak(σ)=S\}$. In \cite{metrics}, Diaz-Lopez, Haymaker, Keough, Park and White considered metrics for unsigned permutations with the same peak set. In this paper, we generalize their result by studying Hamming, $l_{\infty}$, and the word metrics on $P^{B}(S;n)$ for all $S$. We also determine the minimum and maximum possible values that these metrics can achieve in these subsets of $S^B_n$. |
| title | Metrics on Signed Permutations with the Same Peak Set |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2508.15120 |