Number of $A+B\ne C$ solutions in abelian groups and application to counting independent sets in hypergraphs

Aliaksei Semchankau, Dmitry Shabanov, Ilya Shkredov

The paper deals with a problem of Additive Combinatorics. Let $\mathbf{G}$ be a finite abelian group of order $N$. We prove that the number of subset triples $A,B,C\subset {\mathb…