On the number of sum-free triplets of sets

We count the ordered sum-free triplets of subsets in the group Z/pZ, i.e., the triplets (A, B, C) of sets A, B, C subset of Z/pZ for which the equation a + b = c has no solution with a is an element of A, b is an element of B and c is an element of C. Our main theorem improves on a recent result by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our proof relates previous results on the number of independent sets of regular graphs by Kahn; Perarnau and Perkins; and Csikvari to produce explicit estimates on smaller order terms. We also obtain estimates for the number of sum-free triplets of subsets in a general abelian group.