Additive structure in convex translates

2023/02/27 by Currier, Gabriel, Solymosi, Jozsef, White, Ethan Patrick
#05D99 #52C10 #52C30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.13949

Abstract

Let P be a set of points in the plane, and S a strictly convex set of points. In this note, we show that if P contains many translates of S, then these translates must come from a generalized arithmetic progression of low dimension. We also discuss an application to the unit distance conjecture.

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