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Attempts to Count k-Sets

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

Abstract

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.

Keywords

General Position Middle Level Balance Line Edge Crossing Dual Setting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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