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. 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.
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