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arXiv · 1412.7025

On the number of rich lines in high dimensional real vector spaces

Marton Hablicsek·Zachary Scherr
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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.

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Marton Hablicsek, Zachary Scherr. 2021-02-13. On the number of rich lines in high dimensional real vector spaces. https://doi.org/10.1007/s00454-016-9774-6

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