## On a Question of Bourgain about Geometric Incidences

- József Solymosi, Csaba D. Tóth
- Combinatorics, Probability & Computing
- 2008

@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} }

- Published in Discrete & Computational Geometry 2006
DOI:10.1007/s00454-006-1232-4

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.