Symmetric Schroder paths and restricted involutions
| dc.creator | Deng, Eva Y. P. | |
| dc.creator | Dukes, Mark | |
| dc.creator | Mansour, Toufik | |
| dc.creator | Wu, Susan Y. J. | |
| dc.date | 2008-10-29 | |
| dc.date.accessioned | 2026-07-07T10:13:51Z | |
| dc.date.available | 2026-07-07T10:13:51Z | |
| dc.description | Let $A_k$ be the set of permutations in the symmetric group $S_k$ with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns $A_k$. We present a bijection between symmetric Schroder paths of length $2n$ and involutions of length $n+1$ avoiding $\mathcal{A}_4$. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of steps in the symmetric Schroder path of a particular type. For each $k> 2$ we determine the generating function for the number of involutions avoiding the subsequences in $A_k$, according to length, first entry and number of fixed points. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0810.5189 | |
| dc.identifier | http://arxiv.org/abs/0810.5189 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172675 | |
| dc.subject | Combinatorics | |
| dc.title | Symmetric Schroder paths and restricted involutions | |
| dc.type | text |