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 ⩾ k 2 + 2 k 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.