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

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

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 L2[0, 1]m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kre˘ın and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.

Original language	English
Number of pages	12
Publication status	Published - Jun 2006
Event	18th International Conference on Formal Power Series & Algebraic Combinatorics - University of California, San Diego, San Diego, United States Duration: 19 Jun 2006 → 23 Jun 2006

Conference

Conference	18th International Conference on Formal Power Series & Algebraic Combinatorics
Country/Territory	United States
City	San Diego
Period	19/06/06 → 23/06/06

Keywords

pattern avoiding
pattern avoiding permutations
permutations

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 L2[0, 1]m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kre˘ın and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.",

keywords = "pattern avoiding, pattern avoiding permutations, permutations",

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

year = "2006",

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language = "English",

note = "18th International Conference on Formal Power Series & Algebraic Combinatorics ; Conference date: 19-06-2006 Through 23-06-2006",

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T1 - A spectral approach to pattern-avoiding permutations

AU - Ehrenborg, Richard

AU - Kitaev, Sergey

AU - Perry, Peter

PY - 2006/6

Y1 - 2006/6

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 L2[0, 1]m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kre˘ın 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 L2[0, 1]m determines the asymptotic behavior of such permutations. Moreover, using an operator version of the classical Frobenius-Perron theorem due to Kre˘ın and Rutman, we prove asymptotic results for large classes of patterns S. This extends previously known results of Elizalde.

KW - pattern avoiding

KW - pattern avoiding permutations

KW - permutations

UR - http://garsia.math.yorku.ca/fpsac06/en/contrib_papers.html

M3 - Paper

T2 - 18th International Conference on Formal Power Series & Algebraic Combinatorics

Y2 - 19 June 2006 through 23 June 2006

ER -

A spectral approach to pattern-avoiding permutations

Abstract

Conference

Keywords

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