Generalized pattern avoidance with additional restrictions
| dc.creator | Kitaev, Sergey | |
| dc.date | 2002-05-20 | |
| dc.date.accessioned | 2026-07-07T04:48:36Z | |
| dc.date.available | 2026-07-07T04:48:36Z | |
| dc.description | Babson and Steingr\'ımsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider n-permutations that avoid the generalized pattern 1-32 and whose k rightmost letters form an increasing subword. The number of such permutations is a linear combination of Bell numbers. We find a bijection between these permutations and all partitions of an $(n-1)$-element set with one subset marked that satisfy certain additional conditions. Also we find the e.g.f. for the number of permutations that avoid a generalized 3-pattern with no dashes and whose k leftmost or k rightmost letters form either an increasing or decreasing subword. Moreover, we find a bijection between n-permutations that avoid the pattern 132 and begin with the pattern 12 and increasing rooted trimmed trees with n+1 nodes. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0205215 | |
| dc.identifier | http://arxiv.org/abs/math/0205215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64111 | |
| dc.subject | Combinatorics | |
| dc.title | Generalized pattern avoidance with additional restrictions | |
| dc.type | text |