132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

Eric S. Egge; Toufik Mansour

doi:10.1016/j.dam.2003.12.007

132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

Eric S. Egge, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the recursive structures of the set of two-stack sortable permutations which avoid 132 and the set of two-stack sortable permutations which contain 132 exactly once. Using these results and standard generating function techniques, we enumerate two-stack sortable permutations which avoid (or contain exactly once) 132 and which avoid (or contain exactly once) an arbitrary permutation τ. In most cases the number of such permutations is given by a simple formula involving Fibonacci or Pell numbers.

Original language	English
Pages (from-to)	72-83
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	143
Issue number	1-3
DOIs	https://doi.org/10.1016/j.dam.2003.12.007
State	Published - 30 Sep 2004

Keywords

Fibonacci number
Forbidden subsequence
Pattern-avoiding permutation
Pell number
Restricted permutation
Two-stack sortable permutation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2003.12.007

Cite this

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AB - We describe the recursive structures of the set of two-stack sortable permutations which avoid 132 and the set of two-stack sortable permutations which contain 132 exactly once. Using these results and standard generating function techniques, we enumerate two-stack sortable permutations which avoid (or contain exactly once) 132 and which avoid (or contain exactly once) an arbitrary permutation τ. In most cases the number of such permutations is given by a simple formula involving Fibonacci or Pell numbers.

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KW - Forbidden subsequence

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132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

Abstract

Keywords

ASJC Scopus subject areas

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