A combinatorial property of points and ellipsoids
Let \({\mathbb{R}}^ d\) be d-dimensional Euclidean space. The authors prove that there exists a constant \(c_ d>0\) with the following property: for every finite set \(X\subset {\mathbb{R}}^ d\) there is \(Y\subset X\) with at most \(\lfloor (1/4)d(d+3)\rfloor +1\) points such that the arbitrary ellipsoid \(E\supset Y\) contains at least \(c_ d| X|\) points. It is also shown that the bound of the number of points of Y is best possible.
scientific article; zbMATH DE number 4142920