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Beyond sum-free sets in the natural numbers
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dc.contributor.author | Huczynska, Sophie | |
dc.date.accessioned | 2014-07-09T12:01:01Z | |
dc.date.available | 2014-07-09T12:01:01Z | |
dc.date.issued | 2014-02-07 | |
dc.identifier | 108164447 | |
dc.identifier | c5322e45-4a27-4c23-9743-35ed2a040395 | |
dc.identifier | 84893545619 | |
dc.identifier | 000331196200001 | |
dc.identifier.citation | Huczynska , S 2014 , ' Beyond sum-free sets in the natural numbers ' , Electronic Journal of Combinatorics , vol. 21 , no. 1 . | en |
dc.identifier.issn | 1097-1440 | |
dc.identifier.other | ORCID: /0000-0002-0626-7932/work/74117789 | |
dc.identifier.uri | https://hdl.handle.net/10023/4986 | |
dc.description.abstract | For 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.format.extent | 20 | |
dc.format.extent | 306674 | |
dc.language.iso | eng | |
dc.relation.ispartof | Electronic Journal of Combinatorics | en |
dc.subject | Sum-free sets | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Beyond sum-free sets in the natural numbers | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i1p21 | en |
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