Dominance Order - Generalizations

Generalizations

Partitions of n can be graphically represented by Young diagrams on n boxes. Standard Young tableaux are certain ways to fill Young diagrams with numbers, and a partial order on them (sometimes called the dominance order on Young tableaux) can be defined in terms of the dominance order on the Young diagrams. For a Young tableau T to dominate another Young tableau S, the shape of T must dominate that of S 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.