Patterns in random permutations avoiding the pattern 321

Svante Janson

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arXiv · 1709.08427

Patterns in random permutations avoiding the pattern 321

Svante Janson

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Abstract

We consider a random permutation drawn from the set of 321-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{m+\ell}$ where $m$ is the length of $\sigma$ and $\ell$ is the number of blocks in it. The limit is not normal, and can be expressed as a functional of a Brownian excursion.

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Svante Janson. 2017-09-25. Patterns in random permutations avoiding the pattern 321. https://arxiv.org/abs/1709.08427

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