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arXiv · 1401.5679

Patterns in random permutations avoiding the pattern 132

Svante Janson
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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 $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where $\lambda(\sigma)$ is the length of $\sigma$ 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.

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Svante Janson. 2014-01-22. Patterns in random permutations avoiding the pattern 132. https://doi.org/10.1017/s0963548316000171

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