Cyclically consecutive permutation avoidance

Richard Ehrenborg

doi:10.1137/130946848

Cyclically consecutive permutation avoidance

Richard Ehrenborg

Mathematics

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

1 Scopus citations

Abstract

We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σ^∞_k=-∞ (3/2φ(k+1/3)ⁿ for n ≤ 2.

Original language	English
Pages (from-to)	1385-1390
Number of pages	6
Journal	SIAM Journal on Discrete Mathematics
Volume	30
Issue number	3
DOIs	https://doi.org/10.1137/130946848
State	Published - 2016

Bibliographical note

Publisher Copyright:
Copyright © by SIAM.

Keywords

Cyclic consecutive pattern avoidance
Integral operators
Spectrum
Trace class operators

ASJC Scopus subject areas

General Mathematics

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10.1137/130946848

Cite this

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title = "Cyclically consecutive permutation avoidance",

abstract = "We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σ∞k=-∞ (3/2φ(k+1/3)n for n ≤ 2.",

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language = "English",

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AB - We give an explicit formula for the number of permutations that cyclically avoid a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in οn is given by n! times the convergent series Σ∞k=-∞ (3/2φ(k+1/3)n for n ≤ 2.

KW - Cyclic consecutive pattern avoidance

KW - Integral operators

KW - Spectrum

KW - Trace class operators

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JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 3

ER -

Cyclically consecutive permutation avoidance

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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