Nearly Equal Distances in the Plane

P. Erdős, Endre Makai, János Pach

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

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
Volume2
Issue number4
DOIs
Publication statusPublished - 1993

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ASJC Scopus subject areas

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

Cite this

Nearly Equal Distances in the Plane. / Erdős, P.; Makai, Endre; Pach, János.

In: Combinatorics Probability and Computing, Vol. 2, No. 4, 1993, p. 401-408.

Research output: Contribution to journal › Article

Erdős, P, Makai, E & Pach, J 1993, 'Nearly Equal Distances in the Plane', Combinatorics Probability and Computing, vol. 2, no. 4, pp. 401-408. https://doi.org/10.1017/S0963548300000791
Erdős P, Makai E, Pach J. Nearly Equal Distances in the Plane. Combinatorics Probability and Computing. 1993;2(4):401-408. https://doi.org/10.1017/S0963548300000791
Erdős, P. ; Makai, Endre ; Pach, János. / Nearly Equal Distances in the Plane. In: Combinatorics Probability and Computing. 1993 ; Vol. 2, No. 4. pp. 401-408.
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