On the general no-three-in-line problem

2021/06/29 by Theophilus Agama, Agama, Theophilus
Computer Science · #52Cxx #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2106.15621

openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the number of points that can be placed in the grid n× n× ⋯ × n~(d~times)=n^d for all d∈ ℕ with d≥ 2 so that no three points are collinear satisfies the lower bound ≫ n^d-1√[2d]d.This extends the result of the no-three-in-line problem to all dimension d≥ 3.

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