Refined Restricted Permutations
By Aaron Robertson, D. Saracino, Doron Zeilberger. 2002
53 citations recorded by the source corpus.
Abstract. Define $ S_{k}^n (\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_{k}^n (\alpha) $ be the size of $ S_{k}^n (\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)\quad\mathrm{and}\quad s_{n}^{k}(231) = s_{n}^{k}(312)\quad\mathrm{for\quad all}\quad 0\leq k\leq n $.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/458caba61415ac1fc52f42af48e286928f48b42d
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Classification of bijections between 321- and 132-avoiding permutations (2008, background): “[14] that fixed points have the same distribution on 123- and 132avoiding permutations.”