Two theorems on point-flat incidences

2017/07/31 by Ben Lund, Lund, Ben · 3 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Advanced Graph Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1708.00039

Abstract

We improve the theorem of Beck giving a lower bound on the number of k-flats spanned by a set of points in real space, and improve the bound of Elekes and Tóth on the number of incidences between points and k-flats in real space.

Cited by

• On subsets of lattice cubes avoiding affine and spherical degeneracies
• A note on the largest bipartite subgraph in point-hyperplane incidence graphs
• Nondegenerate spheres in four dimensions

Related

• Incidences with curves in R^d
• Incidence Theorems and Their Applications
• Incidence bounds and applications over finite fields
• A short proof of Rudnev's point-plane incidence bound
• Sphere intersections and incidences over finite fields