A spectral approach to pattern-avoiding permutations

Richard Ehrenborg; Sergey Kitaev; Peter Perry

A spectral approach to pattern-avoiding permutations

Richard Ehrenborg, Sergey Kitaev, Peter Perry

Mathematics

Research output: Contribution to conference › Paper › peer-review

3 Scopus citations

Abstract

We study the number of permutations in the symmetric group on n elements that avoid consecutive patterns S. We show that the spectrum of an associated integral operator on the space L ²[0, 1] ^m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kreǐn and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.

Original language	English
Pages	457-468
Number of pages	12
State	Published - 2006
Event	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duration: Jun 19 2006 → Jun 23 2006

Conference

Conference	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
Country/Territory	United States
City	San Diego, CA
Period	6/19/06 → 6/23/06

Keywords

Consecutive pattern avoidance
Eigenfunction expansion
Eigenvalues
Integral operators

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "A spectral approach to pattern-avoiding permutations",

abstract = "We study the number of permutations in the symmetric group on n elements that avoid consecutive patterns S. We show that the spectrum of an associated integral operator on the space L 2[0, 1] m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kreǐn and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.",

keywords = "Consecutive pattern avoidance, Eigenfunction expansion, Eigenvalues, Integral operators",

author = "Richard Ehrenborg and Sergey Kitaev and Peter Perry",

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T1 - A spectral approach to pattern-avoiding permutations

AU - Ehrenborg, Richard

AU - Kitaev, Sergey

AU - Perry, Peter

PY - 2006

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N2 - We study the number of permutations in the symmetric group on n elements that avoid consecutive patterns S. We show that the spectrum of an associated integral operator on the space L 2[0, 1] m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kreǐn and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.

AB - We study the number of permutations in the symmetric group on n elements that avoid consecutive patterns S. We show that the spectrum of an associated integral operator on the space L 2[0, 1] m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kreǐn and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.

KW - Consecutive pattern avoidance

KW - Eigenfunction expansion

KW - Eigenvalues

KW - Integral operators

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M3 - Paper

AN - SCOPUS:84860611681

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EP - 468

T2 - 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006

Y2 - 19 June 2006 through 23 June 2006

ER -

A spectral approach to pattern-avoiding permutations

Abstract

Conference

Keywords

ASJC Scopus subject areas

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