K-sets in four dimensions Academic Article uri icon


  • Abstract We show, with an elementary proof, that the number of halving simplices in a set of n points in ℝ 4 in general position is O (n 4-2/45). This improves the previous bound of O (n 4-1/13^{4}). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

publication date

  • January 1, 2006