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The repeated (popular) distances problem: lower bounds on how often a single distance occurs among pairs of a finite point set, including guarantees that every large subset contains a popular distance, constructions (e.g. lattice-based) attaining such bounds, and the dual relation to the Erdős distinct distances problem. Claims only about counting unit distances or the maximum number of distinct d

There exist n-point planar sets where every subset has a distance repeated at least c|A|^2/n^(1-delta) times.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Discrete geometryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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