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Abstract
Given a linear equation L, a set of A integers is Lfree if does not contain any ‘nontrivial’ solutions to L. This notion incorporates many central topics in combinatorial number theory such as sumfree and progressionfree sets. In this paper we initiate the study of (parameterised) complexity questions involving Lfree sets of integers. The main questions we consider involve deciding whether a finite set of integers A has an Lfree subset of a given size, and counting all such Lfree subsets. We also raise a number of open problems.
Original language  English 

Pages (fromto)  219238 
Journal  Discrete Applied Mathematics 
Volume  243 
Early online date  26 Mar 2018 
DOIs  
Publication status  Published  10 Jul 2018 
Keywords
 (Parameterised) complexity
 Solutionfree sets
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Dive into the research topics of 'On the complexity of finding and counting solutionfree sets of integers'. Together they form a unique fingerprint.Projects
 1 Finished

EPSRC Fellowship: Dr Andrew Treglown  Independence in groups, graphs and the integers
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils