On the complexity of finding and counting solution-free sets of integers.

Given a linear equation L , a set A of integers is L -free if A does not contain any ‘non-trivial’ solutions to L . This notion incorporates many central topics in combinatorial number theory such as sum-free and progression-free sets. In this paper we initiate the study of (parameterised) complexity questions involving L -free sets of integers. The main questions we consider involve deciding whether a finite set of integers A has an L -free subset of a given size, and counting all such L -free subsets. We also raise a number of open problems. [ABSTRACT FROM AUTHOR]