Central Limit Theorems for some Set Partition Statistics

Bobbie Chern, Persi Diaconis, Daniel M. Kane, Robert C. Rhoades

Published 2015-02-03Version 1

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.