Bounding the size of an almost-equidistant set in Euclidean space

Abstract

A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in ${\mathbb{R}}^d$ has cardinality $O(d^{4/3})$.

arXiv comment6 pages