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.
|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||18th International Conference on Formal Power Series & Algebraic Combinatorics|
|Period||19/06/06 → 23/06/06|
- pattern avoiding
- pattern avoiding permutations
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.