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Dense Difference Sets and Their Combinatorial Structure

  • Vitaly BergelsonEmail author
  • Paul Erdős
  • Neil Hindman
  • Tomasz Łuczak
Chapter

Summary

We show that if a set B of positive integers has positive upper density, then its difference set D(B) has extremely rich combinatorial structure, both additively and multiplicatively. If on the other hand only the density of D(B) rather than B is assumed to be positive, one is not guaranteed any multiplicative structure at all and is guaranteed only a modest amount of additive structure.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Vitaly Bergelson
    • 1
    Email author
  • Paul Erdős
    • 2
  • Neil Hindman
    • 3
  • Tomasz Łuczak
    • 4
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  3. 3.Department of MathematicsHoward UniversityWashington, DCUSA
  4. 4.Department of Discrete Mathematics, Faculty of Mathematics and CSAdam Mickiewicz UniversityPoznanPoland

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