On pattern-avoiding permutons
Combinatorics
2024-11-15 v3
Abstract
The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order have a particularly simple structure. Namely, almost every fiber of the disintegration of the permuton (say, along the x-axis) consists only of atoms, at most many, and this bound is sharp. We use this to give a simple proof of the `permutation removal lemma'.
Cite
@article{arxiv.2208.12712,
title = {On pattern-avoiding permutons},
author = {Frederik Garbe and Jan Hladký and Gábor Kun and Kristýna Pekárková},
journal= {arXiv preprint arXiv:2208.12712},
year = {2024}
}
Comments
17 pages, 4 figures. Reorganization of the previous version of the paper by incorporating the appendix into the main body. Addition of relevant citations and contextualization