English

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 nn points in the plane with at most nxn-x points collinear define at least cxnc xn lines for some positive constant cc. 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}
}