Attempts to Count k-Sets

  • Jiří Matoušek
Part of the Graduate Texts in Mathematics book series (GTM, volume 212)


Consider an n-point set X ⊂ R d , and fix an integer k. Call a k-point subset S ⊆ X a k-set of X if there exists an open half-space γ such that S = X ∩ γ; that is, S can be “cut off” by a hyperplane. In this chapter we want to estimate the maximum possible number of k-sets of an n-point set in R d , as a function of n and k.


General Position Middle Level Balance Line Edge Crossing Dual Setting 
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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

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