On the number of rich lines in high dimensional real vector spaces
arXiv:1412.7025 · doi:10.1007/s00454-016-9774-6
Abstract
In this short note we use the polynomial partitioning lemma to strengthen a recent result of Dvir and Gopi about the number of rich lines in high dimensional Euclidean spaces. Our result shows that if there are sufficiently many rich lines incident to a set of points then large fraction of them must be contained in a hyperplane.