Erdős Problem #36
minimum overlap problem

The number of solutions to the equation \(a - b = k\), for \(a \in A\) and \(b \in B\). This represents the "overlap" between sets \(A\) and \(B\) for a given difference \(k\).

The maximum overlap for a given pair of sets \(A\) and \(B\), taken over all possible integer differences \(k\).

Let \(A\) and \(B\) be two complementary subsets, a splitting of the numbers \(\{1, 2, \dots, 2n\}\), such that both have the same cardinality \(n\). Define \(M(n)\) to be the minimum `MaxOverlap` that can be achieved, ranging over all such partitions \((A, B)\).