تقرير
Metrics on permutations with the same peak set
| العنوان: | Metrics on permutations with the same peak set |
|---|---|
| المؤلفون: | Diaz-Lopez, Alexander, Haymaker, Kathryn, Keough, Kathryn, Park, Jeongbin, White, Edward |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05A05 (Primary) |
| الوصف: | Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a peak at index $i$ if $\sigma_{i-1}<\sigma_i>\sigma_{i+1}$. Let $\text{Peak}(\sigma)$ be the set of all peaks of $\sigma$ and define $P(S;n)=\{\sigma\in S_n\, | \,\text{Peak}(\sigma)=S\}$. In this paper we study the Hamming metric, $\ell_\infty$-metric, and Kendall-Tau metric on the sets $P(S;n)$ for all possible $S$, and determine the minimum and maximum possible values that these metrics can attain in these subsets of $S_n$. Comment: 7 pages, 3 tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.10719 |
| رقم الأكسشن: | edsarx.2401.10719 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |