Permutations Containing and Avoiding Certain Patterns

Toufik Mansour
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Toufik Mansour: Haifa University Haifa, Department of Mathematics

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 704-708 from Springer

Abstract: Abstract Let T k m = {σ ∈ S k | σ 1 = m}. We prove that the number of permutations which avoid all patterns in T k m equals (k − 2)!(k − 1) n + l − k for k ≤ n. We then prove that for any τ ∈ T k 1 (or any τ ∈ T k k , the number of permutations which avoid all patterns in T k 1 (or in T k k ) except for τ and contain τ exactly once equals (n + l − k)(k − 1) n − k for k ≤ n. Finally, for any τ ∈ T k m , 2 ≤ m ≤k − 1, this number equals (k − 1)n − k for k ≤ n. These results generalize recent results due to Robertson concerning permutations avoiding 123-pattern and containing 132-pattern exactly once.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_69

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