# The Unapologetic Mathematician

## The Dominance Order on Partitions

December 17, 2010 -

1. […] We will have use of the following technical result about the dominance order: […]

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2. […] biggest problem with the dominance order is that it’s only a partial order. That is, there are some pairs of partitions and so that […]

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3. […] where and . If — where is the group algebra element we’ve defined — then dominates […]

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4. […] can, however, extend the idea of the dominance order to general compositions. As usual we say that […]

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5. […] and , respectively, then we say “dominates” — and we write — if dominates for all […]

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6. […] the dominance order for row tabloids. Of course, in doing so we have to alter our definition of the dominance order on Ferrers diagrams to take columns into account instead of […]

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