Other combinatorial models of minimum-length coset representatives for S ~ ~ n / S n can be given in terms of core partitions (integer partitions in which no hook length is divisible by n) or bounded partitions (integer partitions in which no part is larger than n − 1). Under these correspondences, it can be shown that the weak Bruhat order on S ~ ~ n / S n is isomorphic to a certain subposet of Young's lattice.