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dc.contributor.authorHuczynska, Sophie
dc.identifier.citationHuczynska , S 2014 , ' Beyond sum-free sets in the natural numbers ' , Electronic Journal of Combinatorics , vol. 21 , no. 1 .en
dc.identifier.otherPURE: 108164447
dc.identifier.otherPURE UUID: c5322e45-4a27-4c23-9743-35ed2a040395
dc.identifier.otherScopus: 84893545619
dc.identifier.otherORCID: /0000-0002-0626-7932/work/74117789
dc.identifier.otherWOS: 000331196200001
dc.description.abstractFor an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable r-values, constructive existence results and structural characterizations for sets attaining extremal and near-extremal values.
dc.relation.ispartofElectronic Journal of Combinatoricsen
dc.rights© 2014, the Author. This work is made available online in accordance with the publisher’s policies.en
dc.subjectSum-free setsen
dc.subjectQA Mathematicsen
dc.titleBeyond sum-free sets in the natural numbersen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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