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

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 250, and give empirical results obtained by coding up those techniques. In the sequel we survey the known techniques for finding large 3-free sets of {1, . . . , n} for large n, discuss variants of them, and give empirical results obtained by coding up those techniques and variants. Key words: 3-free sets, Arithmetic Sequence, Arithmetic Progression, van der Waerden's Theorem, non-averaging sets Contents

• Type: Journal
• Year: 2008
• Where: JCSS
• Authors: William I. Gasarch, James Glenn, Clyde P. Kruskal
• Keywords: Arithmetic Progression, JCSS 2008, Large 3-free Sets, Present Techniques