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Combinatorica

, Volume 10, Issue 3, pp 261–269 | Cite as

Variations on the theme of repeated distances

  • P. Erdős
  • J. Pach
Article

Abstract

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ℝd, d≥4. We also give asymptotically tight upper bounds on the total number of occurrences of the “favourite” distances fromn points in ℝd, d≥4. Related results are proved for distances determined byn disjoint compact convex sets in ℝ2.

AMS subject classification (1980)

52 A 37 52 A 40 

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Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • P. Erdős
    • 1
  • J. Pach
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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