71.36 GoodNodeLatticePath

GoodNodeLatticePath(e|H, mu)
GoodNodeLatticePaths(e|H, mu)
LatticePathGoodNodeSequence(e|H, gns)

The function GoodNodeLatticePath returns a sequence of partitions which give a path in the e--good partition lattice from the empty partition to mu. The second function returns the list of all paths in the e--good partition lattice which end in mu, and the third function returns the path corresponding to a given good node sequence gns.

gap> GoodNodeLatticePath(3,3,2,1);
[ [ 1 ], [ 1, 1 ], [ 2, 1 ], [ 2, 1, 1 ], [ 2, 2, 1 ], [ 3, 2, 1 ] ]
gap> GoodNodeLatticePaths(3,3,2,1);
[ [ [ 1 ], [ 1, 1 ], [ 2, 1 ], [ 2, 1, 1 ], [ 2, 2, 1 ], [ 3, 2, 1 ] ], 
  [ [ 1 ], [ 1, 1 ], [ 2, 1 ], [ 2, 2 ], [ 2, 2, 1 ], [ 3, 2, 1 ] ] ]
gap> GoodNodeSequence(4,6,3,2);
[ 0, 3, 1, 0, 2, 2, 3, 3, 0, 1, 1 ]
gap> LatticePathGoodNodeSequence(4,last);
[ [ 1 ], [ 1, 1 ], [ 2, 1 ], [ 2, 2 ], [ 3, 2 ], [ 3, 2, 1 ], [ 4, 2, 1 ], 
  [ 4, 2, 2 ], [ 5, 2, 2 ], [ 6, 2, 2 ], [ 6, 3, 2 ] ] 

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

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