The Additive Structure of Cartesian Products Spanning Few Distinct\n Distances

2016/07/12 by Brandon Hanson, Hanson, Brandon
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Number Theory (math.NT) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1607.03442

openalex publication_date 2016/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Guth and Katz proved that any point set mathcal P in the plane determines\n\Ω(| mathcal P|/\log| mathcal P|) distinct distances. We show that when\nnear to this lower bound, a point set mathcal P of the form A\× A must\nsatisfy |A-A|\≪ |A|^2-1/8.\n

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