A spectral approach to pattern-avoiding permutations

Richard Ehrenborg, Sergey Kitaev, Peter Perry

Research output: Contribution to conferencePaperpeer-review

3 Citations (Scopus)


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


Conference18th International Conference on Formal Power Series & Algebraic Combinatorics
Country/TerritoryUnited States
CitySan Diego


  • pattern avoiding
  • pattern avoiding permutations
  • permutations


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