Geodesic
Beyond sum-free sets in the natural numbers
Sophie Huczynska1
1University of St Andrews
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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For an interval $[1,N] \subseteq \mathbb{N}$, sets $S \subseteq [1,N]$ with the property that $|\{(x,y) \in S^2:x+y \in S\}|=0$, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering $r(S)=|\{(x,y) \in S^2: x+y \in S\}|$, 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.
DOI : 10.37236/2810
Classification : 11B75, 11B13
Mots-clés : sum-free sets

Sophie Huczynska  1

1 University of St Andrews 
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Sophie Huczynska. Beyond sum-free sets in the natural numbers. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/2810

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