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Combinatorica

, Volume 38, Issue 5, pp 1095–1100 | Cite as

The Additive Structure of Cartesian Products Spanning Few Distinct Distances

  • Brandon Hanson
Original Paper

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.

Mathematics Subject Classification (2000)

11P70 52C10 05D99 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Pennsylvania State UniversityUniversity ParkUSA

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