151. Central limit theorems for patterns in multiset permutations and set partitions
- Author
-
Valentin Féray, University of Zurich, Féray, Valentin, Institute of Mathematics University of Zurich, and This work was supported in part by the Swiss National Science Fundation (SNSF), grantnb 200020_172515.
- Subjects
Statistics and Probability ,Dependency (UML) ,Janson ,dependency graphs ,multiset permutations ,central limit theorem ,340 Law ,610 Medicine & health ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,010104 statistics & probability ,510 Mathematics ,Mathematics::Probability ,05A05 ,60F05 ,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] ,FOS: Mathematics ,Mathematics - Combinatorics ,60C05 ,patterns ,1804 Statistics, Probability and Uncertainty ,0101 mathematics ,2613 Statistics and Probability ,MSC 2010 : 60C05, 60F05, 05A05, 05A18 ,Mathematics ,Central limit theorem ,Multiset ,Mathematics::Combinatorics ,Combinatorial probability ,Probability (math.PR) ,010102 general mathematics ,Statistics ,Probability and statistics ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,05A18 ,10123 Institute of Mathematics ,set partitions ,Probability and Uncertainty ,Combinatorics (math.CO) ,multi-set permutations ,Statistics, Probability and Uncertainty ,Mathematics - Probability - 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., Comment: version 2 (52 pages) implements referee's suggestions and uses journal layout
- Published
- 2020