k-Sets in Four Dimensions

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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.

Jirí Matousek, Micha Sharir, Shakhar Smorod

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DCG 2006 | Elementary Proof | General Position | Halving |

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Added	11 Dec 2010
Updated	11 Dec 2010
Type	Journal
Year	2006
Where	DCG
Authors	Jirí Matousek, Micha Sharir, Shakhar Smorodinsky, Uli Wagner

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k-Sets in Four Dimensions

DCG 2006 | Elementary Proof | General Position | Halving |

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