Guth and Katz proved that any point set P in the plane determines Ω(|P|/log |P|) distinct distances. We show that when near to this lower bound, a point set P of the form A × A must satisfy |A-A|≪|A-A|2-1/8.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Computational Mathematics