71.38 InverseLittlewoodRichardsonRule

InverseLittlewoodRichardsonRule(tau)

Returns a list of all pairs of partitions [mu,nu] such that the Littlewood-Richardson coefficient a_{munu}^tau is non-zero (see LittlewoodRichardsonRule). The list returned is unordered and [mu,nu] will appear a_{munu}^tau times in it.

gap> InverseLittlewoodRichardsonRule([3,2,1]);
[ [ [  ],[ 3, 2, 1 ] ],[ [ 1 ],[ 3, 2 ] ],[ [ 1 ],[ 2, 2, 1 ] ], 
  [ [ 1 ],[ 3, 1, 1 ] ],[ [ 1, 1 ],[ 2, 2 ] ],[ [ 1, 1 ],[ 3, 1 ] ], 
  [ [ 1, 1 ],[ 2, 1, 1 ] ],[ [ 1, 1, 1 ],[ 2, 1 ] ],[ [ 2 ],[ 2, 2 ] ], 
  [ [ 2 ],[ 3, 1 ] ],[ [ 2 ],[ 2, 1, 1 ] ],[ [ 2, 1 ],[ 3 ] ], 
  [ [ 2, 1 ],[ 2, 1 ] ],[ [ 2, 1 ],[ 2, 1 ] ],[ [ 2, 1 ],[ 1, 1, 1 ] ], 
  [ [ 2, 1, 1 ],[ 2 ] ],[ [ 2, 1, 1 ],[ 1, 1 ] ],[ [ 2, 2 ],[ 2 ] ], 
  [ [ 2, 2 ],[ 1, 1 ] ],[ [ 2, 2, 1 ],[ 1 ] ],[ [ 3 ],[ 2, 1 ] ], 
  [ [ 3, 1 ],[ 2 ] ],[ [ 3, 1 ],[ 1, 1 ] ],[ [ 3, 1, 1 ],[ 1 ] ], 
  [ [ 3, 2 ],[ 1 ] ],[ [ 3, 2, 1 ],[ ] ] ]

See also LittlewoodRichardsonRule LittlewoodRichardsonRule.

This function requires the package ``specht'' (see RequirePackage).

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