Refined Restricted Permutations
2002; Birkhäuser; Volume: 6; Issue: 3 Linguagem: Inglês
10.1007/s000260200015
ISSN0219-3094
AutoresAaron Robertson, Dan Saracino, Doron Zeilberger,
Tópico(s)Algorithms and Data Compression
ResumoDefine $ 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 $ .
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