Dominance order
![Example of dominance ordering of partitions of n. Here, n = 6, nodes are partitions of 6, edges indicate that the upper node dominates the lower node. While this particular partial ordering is graded, this is not true for the dominance ordering on partitions of any number n > 6.](/Images/godic/202501/09/Dominance_order_partitions_of_63150.png")
![The dominance order on Young tableaux for the partition 6 = 4 + 2](/Images/godic/202501/09/Tableaux_dominance.svg3150.png")
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.