Permutations containing and avoiding certain patterns
| dc.creator | Mansour, T. | |
| dc.date | 1999-11-30 | |
| dc.date | 2000-02-21 | |
| dc.date.accessioned | 2026-07-07T05:32:01Z | |
| dc.date.available | 2026-07-07T05:32:01Z | |
| dc.description | Let T_k^m={σ\in S_k | σ_1=m}. We prove that the number of permutations which avoid all patterns in T_k^m equals (k-2)!(k-1)^{n+1-k} for k <= n. We then prove that for any τin T_k^1 (or any τin T_k^k), the number of permutations which avoid all patterns in T_k^1 (or in T_k^k) except for τand contain τexactly once equals (n+1-k)(k-1)^{n-k} for k <= n. Finally, for any τin T_k^m, 2 <= m <= k-1, this number equals (k-1)^{n-k} for k <= n. These results generalize recent results due to Robertson concerning permutations avoiding 123-pattern and containing 132-pattern exactly once. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/9911243 | |
| dc.identifier | http://arxiv.org/abs/math/9911243 | |
| dc.identifier | Proc. 12th Conference on Formal Power Series and Algebraic combinatorics, 2000, 706-708 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79511 | |
| dc.subject | Combinatorics | |
| dc.title | Permutations containing and avoiding certain patterns | |
| dc.type | text |