Let d1 ≤ d2 ≤ . . . ≤ d(n2) denote the distances determined by n points in the plane. It is shown that min Σi(di+1-di)2=O(n -6/7), where the minimum is taken over all point sets with minimal distance d1 ≥ 1. This bound is asymptotically tight.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics