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Combinatorica

, Volume 10, Issue 2, pp 175–183 | Cite as

On the number of halving planes

  • I. Bárány
  • Z. Füredi
  • L. Lovász
Article

Abstract

LetS ⊂ℝ3 be ann-set in general position. A plane containing three of the points is called a halving plane if it dissectsS into two parts of equal cardinality. It is proved that the number of halving planes is at mostO(n2.998).

As a main tool, for every setY ofn points in the plane a setN of sizeO(n4) is constructed such that the points ofN are distributed almost evenly in the triangles determined byY.

AMS subject classification (1980)

52 A 37 

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Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • I. Bárány
    • 1
  • Z. Füredi
    • 1
  • L. Lovász
    • 2
    • 3
  1. 1.Hungarian Academy of SciencesBudapestHungary
  2. 2.Department of Computer ScienceEötvös Loránd UniversityBudapestHungary
  3. 3.Princeton UniversityPrincetonUSA

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