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Central limit theorems for patterns in multiset permutations and set partitions


Féray, Valentin (2020). Central limit theorems for patterns in multiset permutations and set partitions. Annals of Applied Probability, 30(1):287-323.

Abstract

We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeilberger and Chern, Diaconis, Kane and Rhoades, respectively.

Abstract

We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeilberger and Chern, Diaconis, Kane and Rhoades, respectively.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 February 2020
Deposited On:17 Dec 2020 14:14
Last Modified:24 Jul 2024 01:39
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Additional Information:https://projecteuclid.org/euclid.aoap/1582621225
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/19-aap1502
  • Content: Published Version
  • Language: English