A Central Limit Theorem for Vincular Permutation Patterns
Combinatorics
2023-06-22 v4 Probability
Abstract
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem, we use the method of dependency graphs. The main difficulty is then to estimate the variance of our statistics. We need a lower bound on the variance, for which we introduce a recursive technique based on the law of total variance.
Cite
@article{arxiv.1704.00650,
title = {A Central Limit Theorem for Vincular Permutation Patterns},
author = {Lisa Hofer},
journal= {arXiv preprint arXiv:1704.00650},
year = {2023}
}
Comments
only journal style changes, same content as in v3