Exact bounds on cross-intersecting families (Q5943047)

Let \(\mathcal A\) and \(\mathcal B\) be families of \(k\)- resp. \(l\)-element subsets of an \(n\)-element set. They are called cross-intersecting if \(A\cap B \neq \emptyset\) for all \(A\in \mathcal A\) and \(B \in \mathcal B\). The author determines the maximum of \(|\mathcal A|+|\mathcal B |\) if \(n>k+l\) and \(a\leq |\mathcal A |\leq b\) holds for some natural numbers \(a\) and \(b\). He also gives an algorithm that determines the extremal pairs \((|\mathcal A|, |\mathcal B|)\) if \(a\leq |\mathcal A~|\leq b\) and \(c\leq |\mathcal B|\leq d\).