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TableauSymmetric

TableauSymmetric[tab]
gives the symmetry of the tableau tab as a Strong Generating Set.
  • The Young tableau has to be given as an array. For example, the array {{a, b}, {c, d}} represents the tableau . See also YoungTableauQ.
  • The Strong Generating Set is given in Cycles notation.
  • The resulting Strong Generating Set only captures the mono-term symmetries of the Young tableau.
  • If the tableau is a single row, the result reduces to that of Symmetric.
  • If the tableau is a single column, the result reduces to that of Antisymmetric.
  • If the tableau is a window, the result reduces to that of RiemannSymmetric.
  • The following options can be given:
ManifestSymmetryAntisymmetricwith what manifest symmetry the result is symmetrized
  • Possible settings for ManifestSymmetry include:
Antisymmetricfirst symmetrize rows and then antisymmetrize columns
Symmetricfirst antisymmetrize columns and then symmetrize rows