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Patterns in Random Permutations Avoiding Some Other Patterns (Keynote Speakers)

Author Svante Janson

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ACM Subject Classification
  • Mathematics of computing → Permutations and combinations
  • Mathematics of computing → Probabilistic representations
Keywords
  • Random permutations
  • patterns
  • forbidden patterns
  • limit in distribution
  • U-statistics

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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.

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Svante Janson. Patterns in Random Permutations Avoiding Some Other Patterns (Keynote Speakers). In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.AofA.2018.6

Author Details

Svante Janson
  • Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden

Funding

  • Janson, Svante: Partly supported by the Knut and Alice Wallenberg Foundation

References

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