Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

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.

Full text not available in this repository. Request a copy from the Strathclyde author

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.