On the Dimension of Finite Point Sets I. An Improved Incidence Bound for Proper 3D sets
Gy\"orgy Elekes
TL;DR
This paper enhances the incidence bounds for finite proper 3D point sets, providing tighter constraints on the number of incidences between points and lines in three-dimensional space.
Contribution
It introduces an improved incidence bound specifically for proper 3D point sets, advancing the understanding of geometric incidences in higher dimensions.
Findings
Tighter incidence bounds for proper 3D point sets
Enhanced understanding of geometric configurations in three dimensions
Potential applications in combinatorial geometry
Abstract
We improve the well-known Szemer\'edi-Trotter incidence bound for proper 3--dimensional point sets (defined appropriately)
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Digital Image Processing Techniques · Advanced Numerical Analysis Techniques