TY - JOUR
T1 - Beyond sum-free sets in the natural numbers
AU - Huczynska, Sophie
PY - 2014/2/7
Y1 - 2014/2/7
N2 - 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.
AB - 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.
KW - Sum-free sets
UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i1p21
UR - https://www.scopus.com/pages/publications/84893545619
M3 - Article
SN - 1097-1440
VL - 21
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 1
ER -