as a partition, and moreover the same must hold whenever T and S are first truncated to their sub-tableaux containing entries up to a given value k, for each choice of k. Similarly, there is a dominance order on the set of standard Young bitableaux, which plays a role in the theory of standard monomials. See also Young's lattice Majorization References Enumerative combinatorics Algebraic combinatorics Lattice theory Representation theory