Two Enumerative Results on Cycles of Permutations
| dc.creator | Stanley, Richard P. | |
| dc.date | 2009-01-14 | |
| dc.date.accessioned | 2026-07-07T12:29:31Z | |
| dc.date.available | 2026-07-07T12:29:31Z | |
| dc.description | Answering a question of Bona, it is shown that for n>1 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1,2,...,n} is 1/2 if n is odd and 1/2 - 2/(n-1){n+2) if n is even. Another result concerns the generating function P_h(q) for the number of cycles of the product (1,2,...,n)w, where w ranges over all permutations of 1,2,...,n of cycle type h. A formula is obtained for P_h(q) from which it is proved that the zeros of P_h(q) have real part 0. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0901.2008 | |
| dc.identifier | http://arxiv.org/abs/0901.2008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215904 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15; 05E05 | |
| dc.title | Two Enumerative Results on Cycles of Permutations | |
| dc.type | text |