The Additive Structure of Cartesian Products Spanning Few Distinct Distances
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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.
Mathematics Subject Classification (2000)11P70 52C10 05D99
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