Extremal Subsets of $\{1,...,n\}$ Avoiding Solutions to Linear Equations in Three Variables

Abstract

We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of $\{1,...,n\}$ containing no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form $ax+by=cz$ with $a+b \neq c$.