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

Andrey Kupavskii, Nabil H. Mustafa, Konrad J. Swanepoel

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 $O(d^{4/3})$.

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