Finding large 3-free sets I: The small n case

  • Authors:

  • William Gasarch;James Glenn;Clyde P. Kruskal

  • Affiliations:

  • University of Maryland at College Park, Department of Computer Science, College Park, MD 20742, USA;Loyola College in Maryland, Department of Computer Science, 4501 N. Charles St, Baltimore, MD 21210, USA;University of Maryland at College Park, Department of Computer Science, College Park, MD 20742, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2008

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Abstract

There has been much work on the following question: given n, how large can a subset of {1,...,n} be that has no arithmetic progressions of length 3. We call such sets 3-free. Most of the work has been asymptotic. In this paper we sketch applications of large 3-free sets, present techniques to find large 3-free sets of {1,...,n} for n=