Report
Coalescence Probabilities of Cycle Products
| العنوان: | Coalescence Probabilities of Cycle Products |
|---|---|
| المؤلفون: | Mui, Holden |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | Generalizing a formula of Stanley, we prove combinatorially that the probability that $1, 2, \dots, k$ are contained in the same cycle of a product of two random $n$-cycles is \[\frac{1}{k} + \frac{4 (-1)^n}{ \binom{2k}{k}} \sum_{\substack{1 \leq i \leq k-1 \\ i \not\equiv n \bmod 2}} \binom{2k-1}{k+i} \left(\frac{1}{n+i+1} - \frac{1}{n-i}\right).\] Comment: 23 pages, 12 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2409.01415 |
| رقم الانضمام: | edsarx.2409.01415 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |