Dominance order
In discrete mathematics, dominance order (synonyms: dominance ordering, majorization order, natural ordering) is a partial order on the set of partitions of a positive integer n that plays an important role in algebraic combinatorics and representation theory, especially in the context of symmetric functions and representation theory of the symmetric group. == Definition == If p = (p1,p2,...) and q = (q1,q2,...) are partitions of n, with the parts arranged in the weakly decreasing order, then p precedes q in the dominance order if for any k ≥ 1, the sum of the k largest parts of p is less than or equal to the sum of the k largest parts of q: p ⊴ q if and only if p 1 + ⋯ + p k ≤ q 1 + ⋯ + q k for all k ≥ 1.