The solution to the partition reconstruction problem

Given a partition λ of n, a k-minor of λ is a partition of n−k whose Young diagram fits inside that of λ. We find an explicit function g(n) such that any partition of n can be reconstructed from its set of k-minors if and only if k⩽g(n). In particular, partitions of n⩾k2+2k are uniquely determined by their sets of k-minors. This result completely solves the partition reconstruction problem and also a special case of the character reconstruction problem for finite groups.