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A spectral approach to pattern-avoiding permutations

Ehrenborg, Richard and Kitaev, Sergey and Perry, Peter (2006) A spectral approach to pattern-avoiding permutations. In: 18th International Conference on Formal Power Series & Algebraic Combinatorics, 2006-06-19 - 2006-06-23, University of California, San Diego.

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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 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.