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Refined Restricted Permutations Avoiding Subsets of Patterns of Length Three

✍ Scribed by Toufik Mansour, Aaron Robertson

Book ID: 120770415
Publisher: Springer
Year: 2002
Tongue: English
Weight: 168 KB
Volume: 6
Category: Article
ISSN: 0218-0006
DOI: 10.1007/s000260200013

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Theorem 4.3. For α β ∈ 132 213 213 132 231 312 312, 231 we have s n α β = n2 n-5 for n ≥ 4 and s 3 α β = 1.

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Proving and disproving some earlier conjectures, we give a characterization of the numbers of permutations avoiding each pattern of length 4. Some implications for longer patterns are included.

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