On the Number of Sum-Free Triplets of Sets

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