Refined Restricted Permutations

Robertson, Aaron; Saracino, Dan; Zeilberger, Doron

Refined Restricted Permutations

Authors

Robertson, Aaron

Saracino, Dan

Zeilberger, Doron

Description

Define $S_n^k(α)$ to be the set of permutations of $\{1,2,...,n\}$ with exactly $k$ fixed points which avoid the pattern $α\in S_m$. Let $s_n^k(α)$ be the size of $S_n^k(α)$. We investigate $S_n^0(α)$ for all $α\in S_3$ as well as show that $s_n^k(132)=s_n^k(213)=s_n^k(321)$ and $s_n^k(231)=s_n^k(312)$ for all $0 \leq k \leq n$.
This article is dedicated to the memory of Rodica Simion