Abstract
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. © 2005 Springer Science+Business Media, Inc.
Cite
CITATION STYLE
APA
Matousek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets in four dimensions. Discrete and Computational Geometry, 35(2), 177–191. https://doi.org/10.1007/s00454-005-1200-4
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