تقرير
Pattern containment in random permutations
| العنوان: | Pattern containment in random permutations |
|---|---|
| المؤلفون: | Gill, Jonna |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05A05 |
| الوصف: | This paper studies permutation statistics that count occurrences of patterns. Their expected values on a product of $t$ permutations chosen randomly from $\Gamma \subseteq S_{n}$, where $\Gamma$ is a union of conjugacy classes, are considered. Hultman has described a method for computing such an expected value, denoted $\mathbb{E}_{\Gamma}(s,t)$, of a statistic $s$, when $\Gamma$ is a union of conjugacy classes of $S_{n}$. The only prerequisite is that the mean of $s$ over the conjugacy classes is written as a linear combination of irreducible characters of $S_{n}$. Therefore, the main focus of this article is to express the means of pattern-counting statistics as such linear combinations. A procedure for calculating such expressions for statistics counting occurrences of classical and vincular patterns of length 3 is developed, and is then used to calculate all these expressions. The results can be used to compute $\mathbb{E}_{\Gamma}(s,t)$ for all the above statistics, and for all functions on $S_{n}$ that are linear combinations of them. Comment: This paper is a part of my PhD Thesis which was written 2013 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.07311 |
| رقم الأكسشن: | edsarx.2406.07311 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |