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On the Structure of Pointsets with Many Collinear Triples
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Journal Article
On the Structure of Pointsets with Many Collinear Triples
2024
Overview
It is conjectured that if a finite set of points in the plane contains many collinear triples, then part of the set has a structure. We will show that under some combinatorial conditions, such pointsets have special configurations of triples, proving a case of Elekes’ conjecture. Using the techniques applied in the proof, we show a density version of Jamison’s theorem. If the number of distinct directions between many pairs of points of a point set in a convex position is small, then many points are on a conic.
Publisher
Springer Nature B.V
Subject
