Size of the largest sum-free subset of $[n{]}^3$ and $[n{]}^4$

Abstract

We determine the density of the largest sum-free subset of the lattice cube $\{1,2,\dots ,n{\}}^d$ for $d=3$ and $d=4$. This solves a conjecture of Cameron and Aydinian in dimensions $3$ and $4$.

20 pages, 2 figures