k-Sets in Four Dimensions

We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 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.

• Type: Journal
• Year: 2006
• Where: DCG
• Authors: Jirí Matousek, Micha Sharir, Shakhar Smorodinsky, Uli Wagner
• Keywords: DCG 2006, Elementary Proof, General Position, Halving