A better bound for ordinary triangles

2018/05/17 by Quentin Dubroff, Dubroff, Quentin
Computer Science · Mathematics · #52C10 #52C35 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1805.06954

openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P be a finite set of points in the plane. A c-ordinary triangle is a set of three non-collinear points of P such that each line spanned by the points contains at most c points of P. We show that if P is not contained in the union of two lines and |P| is sufficiently large, then it contains an 11-ordinary triangle. This improves upon a result of Fulek et al., who showed one may take c=12000.

Citations

• Spanned lines and Langer's inequality

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