The Brownian limit of separable permutations

By Frédérique Bassino, Mathilde Bouvel, Valentin F'eray, Lucas Gerin, Adeline Pierrot. Annals of Probability, 2016

68 citations recorded by the source corpus.

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".

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74d202c11bad3fc3a9c21743c6d8b243908a0ede

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Mickaël Maazoun
2. Adeline Pierrot
3. Frédérique Bassino
4. Mathilde Bouvel
5. Valentin F'eray
6. Lucas Gerin

In Discrete Mathematics and Combinatorics

1. Mathilde Bouvel
2. Valentin F'eray

In Mathematical Physics

1. Mickaël Maazoun
2. Adeline Pierrot
3. Frédérique Bassino
4. Mathilde Bouvel
5. Valentin F'eray
6. Lucas Gerin

Citations in the corpus

• Universal limits of substitution-closed permutation classes (2017, background): “For instance, the class Av(2413, 3142) of separable permutations studied in [12] corresponds to the set of all canonical trees built on {⊕, }, i.”