Counting Descent Pairs with Prescribed Tops and Bottoms
| dc.creator | Hall, John T. | |
| dc.creator | Remmel, Jeffrey B. | |
| dc.date | 2006-10-20 | |
| dc.date.accessioned | 2026-07-07T07:29:15Z | |
| dc.date.available | 2026-07-07T07:29:15Z | |
| dc.description | Given sets X and Y of positive integers and a permutation sigma = sigma_1, sigma_2, ..., sigma_n in S_n, an X,Y-descent of sigma is a descent pair sigma_i > sigma_{i+1} whose "top" sigma_i is in X and whose "bottom" sigma_{i+1} is in Y. We give two formulas for the number P_{n,s}^{X,Y} of sigma in S_n with s X,Y-descents. P_{n,s}^{X,Y} is also shown to be a hit number of a certain Ferrers board. This work generalizes results of Kitaev and Remmel on counting descent pairs whose top (or bottom) is equal to 0 mod k. | |
| dc.description | 27 pages, 18 figures | |
| dc.identifier | https://arxiv.org/abs/math/0610608 | |
| dc.identifier | http://arxiv.org/abs/math/0610608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118031 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 (Primary), 05A05, 05A19 (Secondary) | |
| dc.title | Counting Descent Pairs with Prescribed Tops and Bottoms | |
| dc.type | text |