Popular distances in 3-space

Paul Erdos, Gergely Harcos, János Pach

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Abstract

Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn1/3 log log n≤m(n)≤n3/5 β(n), where c>0 is a constant and β(n) is an extremely slowly growing function, related to the inverse of the Ackermann function.

Original languageEnglish
Pages (from-to)95-99
Number of pages5
JournalDiscrete Mathematics
Volume200
Issue number1-3
DOIs
Publication statusPublished - Apr 6 1999

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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