Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences

Toufik Mansour; Gökhan Yıldırım

doi:10.1016/j.aam.2020.102002

Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences

Toufik Mansour, Gökhan Yıldırım

Department of Mathematics

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

Abstract

We study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.

Original language	English
Article number	102002
Journal	Advances in Applied Mathematics
Volume	116
DOIs	https://doi.org/10.1016/j.aam.2020.102002
State	Published - May 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Chebyshev polynomials
Generating functions
Longest increasing subsequence problem
Pattern-avoiding permutations

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2020.102002

Cite this

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title = "Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences",

abstract = "We study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.",

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author = "Toufik Mansour and G{\"o}khan Yıldırım",

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N2 - We study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.

AB - We study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.

KW - Chebyshev polynomials

KW - Generating functions

KW - Longest increasing subsequence problem

KW - Pattern-avoiding permutations

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JO - Advances in Applied Mathematics

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Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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