2022/06/02 by József Solymosi, Solymosi, Jozsef
Computer Science · Mathematics · #05D05 #52C10 #52C30 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2206.00889
openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is conjectured that if a finite set of points in the plane contains many collinear triples then there is some structure in the set. We are going to show that under some combinatorial conditions such pointsets contain 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 pointset in convex position is small, then many points are on a conic.