Chebyshev centers and radius of the set of permutons
Combinatorics
2026-05-20 v2 Metric Geometry
Probability
Abstract
We study the metric geometry of the set of permutons under the rectangular distance . We determine the Chebyshev radius to be 1/4 and characterize all Chebyshev centers: a permuton is a center if and only if it is 1/2- periodic in each coordinate. We also describe permutons that attain the extremal distance 1/4 from a given center.
Cite
@article{arxiv.2602.02889,
title = {Chebyshev centers and radius of the set of permutons},
author = {Balázs Maga},
journal= {arXiv preprint arXiv:2602.02889},
year = {2026}
}
Comments
10 pages, 1 figure. Section 4 restructured and slightly extended