Symmetric_Functions

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title: Symmetric Functions permalink: wiki/Symmetric_Functions/ layout: wiki

Expand the SchurRings package and optimize some of the existing functions. Implement in M2 (some of) the functions from John Stembridge's SF package

To Do List

• Add h-basis and improve conversion between e-, p- and h- bases.
• Allow memoization for Jacobi-Trudi.
• Implement two methods for conversion to s-basis
  • using Stembridge's idea.
  • using the facilities of the schurRing type.
• Plethysm.
• Characters of the symmetric group.
  • Conversion between characters and symmetric functions.
  • Inner tensor product of S_n-representations/symmetric functions.
  • Scalar product of characters/symmetric functions.
• Allow schurRings over arbitrary base rings.

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