K-sets in four dimensions

Jiri Matousek, Micha Sharir, Shakhar Smorodinsky, Uli Wagner

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

Original languageEnglish
Pages (from-to)177-191
Number of pages15
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - 1 Jan 2006
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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