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On Permutation Pattern Classes with Two Restrictions Only

✍ Scribed by M. D. Atkinson

Publisher
Springer
Year
2007
Tongue
English
Weight
214 KB
Volume
11
Category
Article
ISSN
0218-0006

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πŸ“œ SIMILAR VOLUMES

Permutations with Restricted Patterns an
Permutations with Restricted Patterns and Dyck Paths
✍ C. Krattenthaler πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 190 KB

We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding permutations with a given number of occurrences of the pattern 12 k follow directly from old results on the enu

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✍ Aaron Robertson πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 151 KB

Theorem 4.3. For Ξ± Ξ² ∈ 132 213 213 132 231 312 312, 231 we have s n Ξ± Ξ² = n2 n-5 for n β‰₯ 4 and s 3 Ξ± Ξ² = 1.

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Permutations with one or two 132-subsequences
✍ MiklΓ³s BΓ³na πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 370 KB

We prove a strikingly simple formula for the number of permutations containing exactly one subsequence of type 132. We show that this number equals the number of partitions of a convex (n + 1 )-gon into n -2 parts by noncrossing diagonals. We also prove a recursive formula for the number d, of those