Finding Large Sets Without Arithmetic Progressions of Length Three: An Empirical View and Survey II

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, review the literature of how to construct large 3-free sets, and present empirical studies on how large such sets actually are. The two main questions considered are (1) How large can a 3-free set be when n is small, and (2) How do the methods in the literature compare to each other? In particular, when do the ones that are asymptotically better actually yield larger sets? (This paper overlaps with our previous paper with the title { Finding Large 3-Free Sets I: the Small n Case}.)