Proves non-Euclidean analogs of the Erdős-Anning theorem on integer-distance point sets and resolves Guy's equilateral dimension question via additively weighted Voronoi diagrams.
Eppstein, Forbidden Configurations in Discrete Geometry, Cambridge University Press, Cambridge
2 Pith papers cite this work. Polarity classification is still indexing.
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The maximum density of a no-three-in-line set on the checkerboard is at most the middle real root α of the cubic equation 401α³ - 1744α² + 2240α - 768 = 0.
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Non-Euclidean Erd\H{o}s-Anning Theorems
Proves non-Euclidean analogs of the Erdős-Anning theorem on integer-distance point sets and resolves Guy's equilateral dimension question via additively weighted Voronoi diagrams.
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No-three-in-line sets on the checkerboard grid
The maximum density of a no-three-in-line set on the checkerboard is at most the middle real root α of the cubic equation 401α³ - 1744α² + 2240α - 768 = 0.