Central limit theorems for patterns in multiset permutations and set partitions
Combinatorics
2020-02-26 v2 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.
Cite
@article{arxiv.1811.03923,
title = {Central limit theorems for patterns in multiset permutations and set partitions},
author = {Valentin Féray},
journal= {arXiv preprint arXiv:1811.03923},
year = {2020}
}
Comments
version 2 (52 pages) implements referee's suggestions and uses journal layout