Two theorems on point-flat incidences

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.

References in corpus (3)

• Incidences between points on a variety and planes in R^3
• Extending Erdős- Beck's theorem to higher dimensions
• Essential dimension and the flats spanned by a point set

Cited by in corpus (2)

• Nondegenerate spheres in four dimensions
• A note on the largest bipartite subgraph in point-hyperplane incidence graphs