The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Abstract

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.

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Correspondence to Brandon Hanson.

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Hanson, B. The Additive Structure of Cartesian Products Spanning Few Distinct Distances. Combinatorica 38, 1095–1100 (2018). https://doi.org/10.1007/s00493-016-3665-6

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Mathematics Subject Classification (2000)

  • 11P70
  • 52C10
  • 05D99