English

On almost-equidistant sets

Metric Geometry 2019-04-18 v3 Combinatorics

Abstract

A finite set of points in Rd\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 Rd\mathbb R^d has cardinality at most 5d13/95d^{13/9}.

Keywords

Cite

@article{arxiv.1707.00295,
  title  = {On almost-equidistant sets},
  author = {Alexandr Polyanskii},
  journal= {arXiv preprint arXiv:1707.00295},
  year   = {2019}
}

Comments

v3: 8 pages, minor corrections. Key words: equilateral sets, almost-equidistant sets, unit distance graph