Refined Restricted Permutations

Aaron Robertson, Dan Saracino, Doron Zeilberger

Define $S_n^k(\alpha )$ to be the set of permutations of $\{1,2,...,n\}$ with exactly $k$ fixed points which avoid the pattern $\alpha \in S_m$. Let $s_n^k(\alpha )$ be the size of $S_n^k(\alpha )$. We in…