Continued fractions, statistics, and generalized patterns
| dc.creator | Mansour, T. | |
| dc.date | 2001-10-03 | |
| dc.date | 2001-10-20 | |
| dc.date.accessioned | 2026-07-07T04:43:39Z | |
| dc.date.available | 2026-07-07T04:43:39Z | |
| dc.description | Recently, Babson and Steingrimsson (see \cite{BS}) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following \cite{BCS}, let $e_kπ$ (respectively; $f_kπ$) be the number of the occurrences of the generalized pattern $12\mn3\mn...\mn k$ (respectively; $21\mn3\mn...\mn k$) in $π$. In the present note, we study the distribution of the statistics $e_kπ$ and $f_kπ$ in a permutation avoiding the classical pattern $1\mn3\mn2$. Also we present an applications, which relates the Narayana numbers, Catalan numbers, and increasing subsequences, to permutations avoiding the classical pattern $1\mn3\mn2$ according to a given statistics on $e_kπ$, or on $f_kπ$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0110040 | |
| dc.identifier | http://arxiv.org/abs/math/0110040 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62314 | |
| dc.subject | Combinatorics | |
| dc.title | Continued fractions, statistics, and generalized patterns | |
| dc.type | text |