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

Meeks, K. and Treglown, A. (2018) On the complexity of finding and counting solution-free sets of integers. Discrete Applied Mathematics, 243, pp. 219-238. (doi:10.1016/j.dam.2018.02.008)

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Abstract

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.

Item Type:Articles
Additional Information:The first author is supported by a Personal Research Fellowship from the Royal Society of Edinburgh, funded by the Scottish Government, and the second author is supported by EPSRC grant EP/M016641/1.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty
Authors: Meeks, K., and Treglown, A.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Discrete Applied Mathematics
Publisher:Elsevier
ISSN:0166-218X
ISSN (Online):1872-6771
Published Online:26 March 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Discrete Applied Mathematics 243:219-238
Publisher Policy:Reproduced under a Creative Commons License

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