D. Saracino

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math.CO2002

Refined Restricted Involutions

Emeric Deutsch, Aaron Robertson, Dan Saracino

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…

math.CO2002

Refined Restricted Permutations

Aaron Robertson, Dan Saracino, Doron Zeilberger

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 in…