Refined Restricted Permutations

Details Refined Restricted Permutations Refined Restricted Permutations

2002-03-04

arxiv.org/abs/math/0203033v1

Mathematics

Combinatorics

This article is dedicated to the memory of Rodica Simion

Scientific paper

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 investigate $S_n^0(\alpha)$ for all $\alpha \in S_3$ 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 $0 \leq k \leq n$.

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