On multi-avoidance of generalized patterns
| dc.creator | Mansour, T. | |
| dc.creator | Kitaev, S. | |
| dc.date | 2002-09-25 | |
| dc.date.accessioned | 2026-07-07T04:51:14Z | |
| dc.date.available | 2026-07-07T04:51:14Z | |
| dc.description | In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In three essentially different cases, the numbers of such $n$-permutations are $2^{n-1}$, the number of involutions in $\mathcal{S}_n$, and $2E_n$, where $E_n$ is the $n$-th Euler number. In this paper we give recurrence relations for the remaining three essentially different cases. To complete the descriptions in [Kit3] and [KitMans], we consider avoidance of a pattern of the form $x-y-z$ (a classical 3-pattern) and beginning or ending with an increasing or decreasing pattern. Moreover, we generalize this problem: we demand that a permutation must avoid a 3-pattern, begin with a certain pattern and end with a certain pattern simultaneously. We find the number of such permutations in case of avoiding an arbitrary generalized 3-pattern and beginning and ending with increasing or decreasing patterns. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209340 | |
| dc.identifier | http://arxiv.org/abs/math/0209340 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65071 | |
| dc.subject | Combinatorics | |
| dc.title | On multi-avoidance of generalized patterns | |
| dc.type | text |