A spectral approach to pattern-avoiding permutations

Richard Ehrenborg, Sergey Kitaev, Peter Perry

Research output: Contribution to conferencePaper

3 Citations (Scopus)

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 languageEnglish
Number of pages12
Publication statusPublished - Jun 2006
Event18th International Conference on Formal Power Series & Algebraic Combinatorics - University of California, San Diego, San Diego, United States
Duration: 19 Jun 200623 Jun 2006

Conference

Conference18th International Conference on Formal Power Series & Algebraic Combinatorics
CountryUnited States
CitySan Diego
Period19/06/0623/06/06

Fingerprint

Pattern-avoiding Permutation
Permutation
Perron-Frobenius Theorem
Symmetric group
Integral Operator
Consecutive
Asymptotic Behavior
Operator

Keywords

  • pattern avoiding
  • pattern avoiding permutations
  • permutations

Cite this

Ehrenborg, R., Kitaev, S., & Perry, P. (2006). A spectral approach to pattern-avoiding permutations. Paper presented at 18th International Conference on Formal Power Series & Algebraic Combinatorics, San Diego, United States.
Ehrenborg, Richard ; Kitaev, Sergey ; Perry, Peter. / A spectral approach to pattern-avoiding permutations. Paper presented at 18th International Conference on Formal Power Series & Algebraic Combinatorics, San Diego, United States.12 p.
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Ehrenborg, R, Kitaev, S & Perry, P 2006, 'A spectral approach to pattern-avoiding permutations' Paper presented at 18th International Conference on Formal Power Series & Algebraic Combinatorics, San Diego, United States, 19/06/06 - 23/06/06, .

A spectral approach to pattern-avoiding permutations. / Ehrenborg, Richard; Kitaev, Sergey; Perry, Peter.

2006. Paper presented at 18th International Conference on Formal Power Series & Algebraic Combinatorics, San Diego, United States.

Research output: Contribution to conferencePaper

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AU - Perry, Peter

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Ehrenborg R, Kitaev S, Perry P. A spectral approach to pattern-avoiding permutations. 2006. Paper presented at 18th International Conference on Formal Power Series & Algebraic Combinatorics, San Diego, United States.