تقرير
Ewens sampling and invariable generation
| العنوان: | Ewens sampling and invariable generation |
|---|---|
| المؤلفون: | Brito, Gerandy, Fowler, Christopher, Junge, Matthew, Levy, Avi |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Combinatorics, Mathematics - Group Theory, 60C05, 12Y05, 68W20, 68W30, 68W40 |
| الوصف: | We study the number of random permutations needed to invariably generate the symmetric group, $S_n$, when the distribution of cycle counts has the strong $\alpha$-logarithmic property. The canonical example is the Ewens sampling formula, for which the number of $k$-cycles relates to a conditioned Poisson random variable with mean $\alpha/k$. The special case $\alpha =1$ corresponds to uniformly random permutations, for which it was recently shown that exactly four are needed. For strong $\alpha$-logarithmic measures, and almost every $\alpha$, we show that precisely $\left\lceil ( 1- \alpha \log 2 )^{-1} \right\rceil$ permutations are needed to invariably generate $S_n$. A corollary is that for many other probability measures on $S_n$ no bounded number of permutations will invariably generate $S_n$ with positive probability. Along the way we generalize classic theorems of Erd\H{o}s, Tehran, Pyber, Luczak and Bovey to permutations obtained from the Ewens sampling formula. Comment: 34 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1610.04212 |
| رقم الأكسشن: | edsarx.1610.04212 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |