K-sets in four dimensions

J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete & Computational Geometry 35 (2006) 177–191.

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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.
Publishing Year
Date Published
2006-02-01
Journal Title
Discrete & Computational Geometry
Volume
35
Issue
2
Page
177 - 191
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Matoušek J, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. Discrete & Computational Geometry. 2006;35(2):177-191. doi:10.1007/s00454-005-1200-4
Matoušek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets in four dimensions. Discrete & Computational Geometry, 35(2), 177–191. https://doi.org/10.1007/s00454-005-1200-4
Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets in Four Dimensions.” Discrete & Computational Geometry 35, no. 2 (2006): 177–91. https://doi.org/10.1007/s00454-005-1200-4.
J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,” Discrete & Computational Geometry, vol. 35, no. 2, pp. 177–191, 2006.
Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions. Discrete & Computational Geometry. 35(2), 177–191.
Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” Discrete & Computational Geometry, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:10.1007/s00454-005-1200-4.

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