Chebyshev centers and radius of the set of permutons
Abstract
We study the metric geometry of the set of permutons under the rectangular distance $d_{\square}$. 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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Geometric Analysis and Curvature Flows
Probability and Statistical Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 February 2026
- Document type
- Preprint