Central Limit Theorems for some Set Partition Statistics
Combinatorics
2015-02-04 v1 Probability
Abstract
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.
Cite
@article{arxiv.1502.00938,
title = {Central Limit Theorems for some Set Partition Statistics},
author = {Bobbie Chern and Persi Diaconis and Daniel M. Kane and Robert C. Rhoades},
journal= {arXiv preprint arXiv:1502.00938},
year = {2015}
}