Hofer, Lisa - A Central Limit Theorem for Vincular Permutation Patterns

dmtcs:3269 - Discrete Mathematics & Theoretical Computer Science, March 26, 2018, Vol. 19 no. 2, Permutation Patterns 2016 - https://doi.org/10.23638/DMTCS-19-2-9
A Central Limit Theorem for Vincular Permutation Patterns

Authors: Hofer, Lisa

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.

Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: March 26, 2018
Submitted on: April 17, 2017
Keywords: Mathematics - Combinatorics,Mathematics - Probability