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URN: urn:nbn:de:0030-drops-88996
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Patterns in Random Permutations Avoiding Some Other Patterns (Keynote Speakers)

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Abstract

Consider a random permutation drawn from the set of permutations of length n that avoid a given set of one or several patterns of length 3. We show that the number of occurrences of another pattern has a limit distribution, after suitable scaling. In several cases, the limit is normal, as it is in the case of unrestricted random permutations; in other cases the limit is a non-normal distribution, depending on the studied pattern. In the case when a single pattern of length 3 is forbidden, the limit distributions can be expressed in terms of a Brownian excursion. The analysis is made case by case; unfortunately, no general method is known, and no general pattern emerges from the results.

BibTeX - Entry

@InProceedings{janson:LIPIcs:2018:8899,
  author =	{Svante Janson},
  title =	{{Patterns in Random Permutations Avoiding Some Other Patterns (Keynote Speakers)}},
  booktitle =	{29th International Conference on Probabilistic,  Combinatorial and Asymptotic Methods for the Analysis of Algorithms  (AofA 2018)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{James Allen Fill and Mark Daniel Ward},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8899},
  URN =		{urn:nbn:de:0030-drops-88996},
  doi =		{10.4230/LIPIcs.AofA.2018.6},
  annote =	{Keywords: Random permutations, patterns, forbidden patterns, limit in distribution, U-statistics}
}

Keywords: Random permutations, patterns, forbidden patterns, limit in distribution, U-statistics
Seminar: 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)
Issue date: 2018
Date of publication: 2018


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