Cancellative pairs of families of sets
A pair \(({\mathcal A}, {\mathcal B})\) of families of \(n\)-element sets is cancellative if, for all \(A, A'\in {\mathcal A}\) and \(B, B'\in {\mathcal B}\), the conditions \(A\backslash B= A'\backslash B\Rightarrow A= A'\) and \(B\backslash A= B'\backslash A\Rightarrow B= B'\) hold. The paper proves that every such pair satisfies \(| {\mathcal A}| |{\mathcal B}|< c^ n\), where \(c\approx 2.3264\). This is related to the well-known conjecture of Erdős and Katona on cancellative families. The proof uses information theoretical tools.
scientific article; zbMATH DE number 773830