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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'' = (''p''1,''p''2,…) and ''q'' = (''q''1,''q''2,…) 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'':
:
In this definition, partitions are extended by appending zero parts at the end as necessary.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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