Refined Restricted Permutations Avoiding Subsets of Patterns of Length Three

Abstract

Define $S_n^k(T)$ to be the set of permutations of $\{1,2,...,n\}$ with exactly $k$ fixed points which avoid all patterns in $T\subseteq S_m$. We enumerate $S_n^k(T)$, $T\subseteq S_3$, for all $|T|\ge 2$ and $0\le k\le n$.