Maximum number of sum-free colorings in finite abelian groups

摘要

An r-coloring of a subset A of a finite abelian group G is called sum-free if it does not induce a monochromatic Schur triple, i.e., a triple of elements a, b, c a A with a + b = c. We investigate kappa (r) ,G, the maximum number of sum-free r-colorings admitted by subsets of G, and our results show a close relationship between kappa (r) ,G and largest sum-free sets of G.