The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Brandon Hanson

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1095-1100
Number of pages6
JournalCombinatorica
Volume38
Issue number5
DOIs
StatePublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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