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.)

Problems with a Point, pp. 257-266 (2019) No AccessChapter 24: If That Were True I Would Know It! A Result in Kolmogorov ComplexityWilliam Gasarch and Clyde KruskalWilliam GasarchUniversity of Maryland, USA and Clyde KruskalUniversity of Maryland, USAhttps://doi.org/10.1142/9789813279735_0024Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Point How to Measure Randomness Intuitively A Short Introduction to Computability Theory Intermediary Sets How to Measure Randomness Formally Is the Kolmogorov Function Intermediary? The Point Reiterated References FiguresReferencesRelatedDetails Problems with a PointMetrics History PDF download