Nearly Equal Distances in the Plane

P. Erdős, Endre Makai, János Pach

Research output: Contribution to journalArticle

4 Citations (Scopus)


For any positive integer k and ε > 0, there exist nk,ε, ck, e > 0 with the following property. Given any system of n > nk,ε points in the plane with minimal distance at least 1 and any t1, t2…, tk ≥ 1, the number of those pairs of points whose distance is between ti and [formula omitted] for some 1 ≤ i ≤ k, is at most (n2/2) (1 − 1/(k+1)+ε). This bound is asymptotically tight.

Original languageEnglish
Pages (from-to)401-408
Number of pages8
JournalCombinatorics Probability and Computing
Issue number4
Publication statusPublished - 1993


ASJC Scopus subject areas

  • Applied Mathematics
  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics

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