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

Producción científica: Paper › revisión exhaustiva

3 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas	457-468
Número de páginas	12
Estado	Published - 2006
Evento	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duración: jun 19 2006 → jun 23 2006

Conference

Conference	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
País/Territorio	United States
Ciudad	San Diego, CA
Período	6/19/06 → 6/23/06

ASJC Scopus subject areas

Algebra and Number Theory

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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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AU - Ehrenborg, Richard

AU - Kitaev, Sergey

AU - Perry, Peter

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

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ER -

A spectral approach to pattern-avoiding permutations

Resumen

Conference

ASJC Scopus subject areas

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