Abstract
For eachd≥1 there is a constantc d>0 such that any finite setX⊂R d contains a subsetYχX, |Y|≤[1/4d(d+3)]+1 having the following property: ifE⊃Y is an ellipsoid, then |E ν X|≥c d |X|.
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On leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary. Supported by a research fellowship from the Science and Engineering Research Council, U.K., and by Hungarian National Foundation for Scientific Research Grant No. 1812.
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Bárány, I., Larman, D.G. A combinatorial property of points and ellipsoids. Discrete Comput Geom 5, 375–382 (1990). https://doi.org/10.1007/BF02187798
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DOI: https://doi.org/10.1007/BF02187798