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Patterns in Random Permutations Avoiding the Pattern 132

Published online by Cambridge University Press:  18 May 2016

SVANTE JANSON*
Affiliation:
Department of Mathematics, Uppsala University, PO box 480, SE-751 06 Uppsala, Sweden (e-mail: svante.janson@math.uu.se), http://www2.math.uu.se/~svante/

Abstract

We consider a random permutation drawn from the set of 132-avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by nλ(σ)/2, where λ(σ) is the length of σ plus the number of descents. The limit is not normal, and can be expressed as a functional of a Brownian excursion. Moments can be found by recursion.

Type
Paper
Copyright
Copyright © Cambridge University Press 2016 

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