Central limit theorems for some set partition statistics

We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n]={1,2,…,n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels.

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 70; pp. 92 - 105
Main Authors Chern, Bobbie, Diaconis, Persi, Kane, Daniel M., Rhoades, Robert C.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2015
Subjects
Crossings
Dimension index
Non-standard central limit theorem
Set partitions
Statistics
Supercharacters
secondary
Dimension index
Crossings
Supercharacters
Non-standard central limit theorem
Statistics
primary
Set partitions
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Summary:We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n]={1,2,…,n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2015.06.008