Exponentially sized pointsets with angles less than 61 degrees

2021/10/05 by Miroslav Marinov, Marinov, Miroslav
Computer Science · Engineering · Mathematics · #51M04 #52C10 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Packing Problems #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2110.02415

openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any set of points in ℝ^d, any three of which form an angle less than \fracπ3 + c, has size (1+Θ(c))^d for sufficiently small c>0. The proof is based on a refinement of an approach by Erdős and Füredi. The lower bound is relying on a problem about large hypegraphs with small edge intersections, while the upper bound is tightly connected to the problem of packing disjoint caps on a sphere.

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