Extending Erd\H{o}s- Beck's theorem to higher dimensions
Combinatorics
2018-10-05 v4
Abstract
Erd\H{o}s-Beck theorem states that points in the plane with at most points collinear define at least lines for some positive constant . In this paper, we will present two ways to extend this result to higher dimensions. Our result has application to point-hyperplane incidences and potential application to the point covering problem.
Keywords
Cite
@article{arxiv.1607.00048,
title = {Extending Erd\H{o}s- Beck's theorem to higher dimensions},
author = {Thao Do},
journal= {arXiv preprint arXiv:1607.00048},
year = {2018}
}