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Mathematics > Probability

arXiv:1401.6230 (math)
[Submitted on 24 Jan 2014 (v1), last revised 9 Nov 2014 (this version, v2)]

Title:Structure of Random 312-Avoiding Permutations

Authors: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.
Comments: 36 pages, 10 figures
Subjects: Probability (math.PR)
MSC classes: 60C05
Cite as: arXiv:1401.6230 [math.PR]
  (or arXiv:1401.6230v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1401.6230

Submission history

From: Lerna Pehlivan [view email]
[v1] Fri, 24 Jan 2014 00:52:49 UTC (194 KB)
[v2] Sun, 9 Nov 2014 04:22:37 UTC (60 KB)
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