The Brownian limit of separable permutations
Probability
2018-10-18 v3 Combinatorics
Abstract
We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton".
Cite
@article{arxiv.1602.04960,
title = {The Brownian limit of separable permutations},
author = {Frédérique Bassino and Mathilde Bouvel and Valentin Féray and Lucas Gerin and Adeline Pierrot},
journal= {arXiv preprint arXiv:1602.04960},
year = {2018}
}
Comments
45 pages, 14 figures, incorporating referee's suggestions