Proves Erdős-Anning theorem holds in hyperbolic space of any dimension and gives quantitative bound O(D(d+1)^D) on integer-distance point sets in E^D or H^D given a general-position subset of diameter d.
Noteonintegraldistances.Discrete & Computational Geometry, 30(2):337–342, 2003
2 Pith papers cite this work, alongside 18 external citations. Polarity classification is still indexing.
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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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Tangent Spheres and Integer Distances
Proves Erdős-Anning theorem holds in hyperbolic space of any dimension and gives quantitative bound O(D(d+1)^D) on integer-distance point sets in E^D or H^D given a general-position subset of diameter d.
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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.