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.

Source : oai:arXiv.org:1704.00650

DOI : 10.23638/DMTCS-19-2-9

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

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