Author:
Liu Hong,Sharifzadeh Maryam,Staden Katherine
Abstract
Let $f(n,r)$ denote the maximum number of colourings of $A \subseteq \lbrace 1,\ldots,n\rbrace$ with $r$ colours such that each colour class is sum-free. Here, a sum is a subset $\lbrace x,y,z\rbrace$ such that $x+y=z$. We show that $f(n,2) = 2^{\lceil n/2\rceil}$, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of $f(n,r)$ for $r \leqslant 5$. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献