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Extending Erdős- Beck's theorem to higher dimensions

2016/06/30 by Thao Do, Do, Thao
Computer Science · Engineering · #3D Modeling in Geospatial Applications #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1607.00048

openalex publication_date 2016/06/30 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

Erdős-Beck theorem states that n points in the plane with at most n-x points collinear define at least c xn lines for some positive constant c. 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.

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