Structure of Random 312-Avoiding Permutations

Neal Madras; Lerna Pehlivan

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arXiv · 1401.6230

Structure of Random 312-Avoiding Permutations

Neal Madras·Lerna Pehlivan

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Abstract

We evaluate the probabilities of various events under the uniform distribution on the set of 312-avoiding permutations of 1,...,N. We derive exact formulas for the probability that the ith element of a random permutation is a specific value less than i, and for joint probabilities of two such events. In addition, we obtain asymptotic approximations to these probabilities for large N when the elements are not close to the boundaries or to each other. We also evaluate the probability that the graph of a random 312-avoiding permutation has k specified decreasing points, and we show that for large N the points below the diagonal look like trajectories of a random walk.

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Neal Madras, Lerna Pehlivan. 2014-01-24. Structure of Random 312-Avoiding Permutations. https://arxiv.org/abs/1401.6230

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