Beyond sum-free sets in the natural numbers
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.
Citation
Huczynska , S 2014 , ' Beyond sum-free sets in the natural numbers ' , Electronic Journal of Combinatorics , vol. 21 , no. 1 .
Publication
Electronic Journal of Combinatorics
Status
Peer reviewed
ISSN
1097-1440Type
Journal article
Collections
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