Distinct distances in the plane (Q5939473)

The paper sets a lower bound \(\Omega(n^{6/7})\) for the number of distinct distances among \(n\) points in the plane, measured from one point to the other \(n-1\) points. This improves the earlier lower bound \(\Omega (n^{4/5})\) from \textit{L. A. Székely} [Comb. Probab. Comput. 6, 353-358 (1997; Zbl 0882.52007)]. Note that recently G. Tardos proved an even stronger lower bound, \(\Omega(n^{{4e \over 5e-1}-o(1)})\) (not published yet).