On almost-equidistant sets
classification
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almost-equidistantmathbbpointscalledcardinalitydistancedistinctfinite
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A finite set of points in $\mathbb R^d$ is called almost-equidistant if among any three distinct points in the set, some two are at unit distance. We prove that an almost-equidistant set in $\mathbb R^d$ has cardinality at most $5d^{13/9}$.
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