Incidences of not-too-degenerate hyperplanes

We present a multi-dimensional generalization of the Szemer´edi-Trotter Theorem, and give a sharp bound on the number of incidences of points and not-too-degenerate hyperplanes in threeor higher-dimensional Euclidean spaces. We call a hyperplane not-too-degenerate if at most a constant portion of its incident points lie in a lower dimensional affine subspace.

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: György Elekes, Csaba D. Tóth
• Keywords: COMPGEOM 2005, Dimensional Affine Subspace, Discrete Geometry, Multi-dimensional Generalization, Sharp Bound