Distinct Distances in Homogeneous Sets in Euclidean Space

@article{Solymosi2006DistinctDI,
  title={Distinct Distances in Homogeneous Sets in Euclidean Space},
  author={J{\'o}zsef Solymosi and Csaba D. T{\'o}th},
  journal={Discrete & Computational Geometry},
  year={2006},
  volume={35},
  pages={537-549}
}
A homogeneous set of n points in the d-dimensional Euclidean space determines at least Ω(n2d/(d 2+1)/ log n) distinct distances for a constant c(d) > 0. In three-space, we slightly improve our general bound and show that a homogeneous set of n points determines at least Ω(n.6071) distinct distances. 

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