Uniformly distributed distances - A geometric application of Janson's inequality

János Pach, Joel Spencer

Research output: Contribution to journalArticlepeer-review

Abstract

Let d1 ≤ d2 ≤ . . . ≤ d(n2) denote the distances determined by n points in the plane. It is shown that min Σi(di+1-di)2=O(n -6/7), where the minimum is taken over all point sets with minimal distance d1 ≥ 1. This bound is asymptotically tight.

Original languageEnglish (US)
Pages (from-to)111-124
Number of pages14
JournalCombinatorica
Volume19
Issue number1
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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