Maximum number of points in general position in a random subset of finite 3-dimensional spaces

2025/03/06 by József Balogh, Haoran Luo, Balogh, József +1 · 2 citations
Mathematics · #05B25 #05C65 #05C80 #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Limits and Structures in Graph Theory #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2503.04102

openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α(\mathbbF_q^d,p) be the maximum possible size of a point set in general position in the p-random subset of \mathbbF_q^d. In this note, we determine the order of magnitude of α(\mathbbF_q³,p) up to a polylogarithmic factor by proving a balanced supersaturation result for the sets of 4 points in the same plane.

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