Refined Restricted Involutions
| dc.creator | Deutsch, Emeric | |
| dc.creator | Robertson, Aaron | |
| dc.creator | Saracino, Dan | |
| dc.date | 2002-12-19 | |
| dc.date.accessioned | 2026-07-07T04:53:55Z | |
| dc.date.available | 2026-07-07T04:53:55Z | |
| dc.description | Define $I_n^k(α)$ to be the set of involutions of $\{1,2,...,n\}$ with exactly $k$ fixed points which avoid the pattern $α\in S_i$, for some $i \geq 2$, and define $I_n^k(\emptyset;α)$ to be the set of involutions of $\{1,2,...,n\}$ with exactly $k$ fixed points which contain the pattern $α\in S_i$, for some $i \geq 2$, exactly once. Let $i_n^k(α)$ be the number of elements in $I_n^k(α)$ and let $i_n^k(\emptyset;α)$ be the number of elements in $I_n^k(\emptyset;α)$. We investigate $I_n^k(α)$ and $I_n^k(\emptyset;α)$ for all $α\in S_3$. In particular, we show that $i_n^k(132)=i_n^k(213)=i_n^k(321)$, $i_n^k(231)=i_n^k(312)$, $i_n^k(\emptyset;132) =i_n^k(\emptyset;213)$, and $i_n^k(\emptyset;231)=i_n^k(\emptyset;312)$ for all $0 \leq k \leq n$. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0212267 | |
| dc.identifier | http://arxiv.org/abs/math/0212267 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66040 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A05 | |
| dc.title | Refined Restricted Involutions | |
| dc.type | text |