The Unapologetic Mathematician

Mathematics for the interested outsider

The Dominance Order on Partitions

December 17, 2010 - Posted by | Algebra, Representation Theory, Representations of Symmetric Groups

6 Comments »

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

    Pingback by The Dominance Lemma « The Unapologetic Mathematician | December 20, 2010 | Reply

  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 […]

    Pingback by The Lexicographic Order on Partitions « The Unapologetic Mathematician | December 21, 2010 | Reply

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

    Pingback by Corollaries of the Sign Lemma « The Unapologetic Mathematician | December 31, 2010 | Reply

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

    Pingback by Compositions « The Unapologetic Mathematician | January 6, 2011 | Reply

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

    Pingback by The Dominance Order on Tabloids « The Unapologetic Mathematician | January 10, 2011 | Reply

  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 […]

    Pingback by The Column Dominance Order « The Unapologetic Mathematician | January 20, 2011 | Reply


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