On fixed points of permutations
| dc.creator | Diaconis, Persi | |
| dc.creator | Fulman, Jason | |
| dc.creator | Guralnick, Robert | |
| dc.date | 2007-08-20 | |
| dc.date.accessioned | 2026-07-07T08:24:24Z | |
| dc.date.available | 2026-07-07T08:24:24Z | |
| dc.description | The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they are trivial -- almost every permutation has no fixed points. For the usual action of the symmetric group on k-sets of 1,2,...,n, the limit is a polynomial in independent Poisson variables. This exhausts all cases. We obtain asymptotic estimates in some examples, and give a survey of related results. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0708.2643 | |
| dc.identifier | http://arxiv.org/abs/0708.2643 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136326 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 20B30, 20B35, 05A16, 60C07 | |
| dc.title | On fixed points of permutations | |
| dc.type | text |