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).
GAP 3.4.4