eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-18
6:1
6:12
10.4230/LIPIcs.AofA.2018.6
article
Patterns in Random Permutations Avoiding Some Other Patterns (Keynote Speakers)
Janson, Svante
1
https://orcid.org/0000-0002-9680-2790
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol110-aofa2018/LIPIcs.AofA.2018.6/LIPIcs.AofA.2018.6.pdf
Random permutations
patterns
forbidden patterns
limit in distribution
U-statistics