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.

Saved in:
Bibliographic Details
Main Authors Chern, Bobbie, Diaconis, Persi, Kane, Daniel M, Rhoades, Robert C
Format Journal Article
LanguageEnglish
Published 03.02.2015
Subjects
Mathematics - Combinatorics
Mathematics - Probability
Online AccessGet full text

Cover

More Information
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.
DOI:10.48550/arxiv.1502.00938