This research aims to determine the density of the largest sum-free subsets in lattice cubes of dimensions 3 and 4.
Analyzed the structure of the lattice cube for dimensions 3 and 4.
Applied combinatorial techniques to establish density results.
Determined exact density values for sum-free subsets in dimensions 3 and 4.
Confirmed the conjecture posed by Cameron and Aydinian.
Abstract
Abstract We determine the density of the largest sum-free subset of the lattice cube \1, 2, , n\^d for d = 3 and d = 4. This solves a conjecture of Cameron and Aydinian in dimensions 3 and 4.