Séminaire de Probabilités commun ICJ/UMPA

Scaling limits of finitely specified permutation classes

par Mickaël Maazoun

Europe/Paris
435 (ENS)

435

ENS

Description

Joint work with F. Bassino, M. Bouvel, V. Féray, L. Gerin, A. Pierrot -- The subject of pattern-avoiding permutations is a classic of enumerative combinatorics, still rich of interesting open problems. We adopt a probabilistic point of view: What does the diagram of a large permutation in a pattern-avoiding class typically look like?  Generalizing previous results, we consider classes that possess a finite specification with regard to the so-called substitution decomposition. We obtain convergence results to either Brownian separable permutons or deterministic limit shapes. In the proof, we use tree encodings and classical analytic combinatorics tools. If I have some time left, I will talk about some computations that we can perform on the limiting objects, with interesting consequences in the discrete.