Advertisement

A Note on Elkin’s Improvement of Behrend’s Construction

  • Ben GreenEmail author
  • Julia Wolf

Summary

We provide a short proof of a recent result of Elkin in which large subsets of \(\{1,\ldots,N\}\) free of three-term progressions are constructed.

Keywords

Arithmetic progressions Roth’s theorem 

Notes

Acknowledgement

The authors are grateful to Tom Sanders for helpful conversations.

References

  1. 1.
    F. Behrend. On sets of integers which contain no three terms in arithmetic progression, Proc. Nat. Acad. Sci., 32:331–332, 1946MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    M. Elkin, An improved construction of progression-free sets, available at http://arxiv.org/abs/0801.4310
  3. 3.
    R. Graham, On the growth of a van der Waerden-like function, Integers, 6:#A29, 2006Google Scholar
  4. 4.
    B. Landman, A. Robertson and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2):#A10, 2005MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre for Mathematical SciencesCambridgeEngland
  2. 2.Mathematical Sciences Research InstituteBerkeleyUSA

Personalised recommendations