71.34 GoodNodeSequence

GoodNodeSequence(e|H, mu)
GoodNodeSequences(e|H, mu)

mu an e--regular partition.

Given an e--regular partition mu of n, a good node sequence for mu is a sequence gns of n residues such that mu has a good node of residue r, where r is the last residue in gns, and the first n-1 residues in gns are a good node sequence for the partition obtained from mu by deleting its (unique) good node with residue r (see GoodNodes GoodNodes). In general, mu will have more than one good node sequence; however, any good node sequence uniquely determines mu (see PartitionGoodNodeSequence PartitionGoodNodeSequence).

gap> H:=Specht(4);; GoodNodeSequence(H,4,3,1);
[ 0, 3, 1, 0, 2, 2, 1, 3 ]
gap> GoodNodeSequence(H,4,3,2);
[ 0, 3, 1, 0, 2, 2, 1, 3, 3 ]
gap> GoodNodeSequence(H,4,4,2);  
[ 0, 3, 1, 0, 2, 2, 1, 3, 3, 2 ]
gap> GoodNodeSequence(H,5,4,2);
[ 0, 3, 1, 0, 2, 2, 1, 3, 3, 2, 0 ]

The function GoodNodeSequences returns the list of all good node sequences for mu.

gap> GoodNodeSequences(H,5,2,1);
[ [ 0, 1, 2, 3, 3, 2, 0, 0 ], [ 0, 3, 1, 2, 2, 3, 0, 0 ], 
  [ 0, 1, 3, 2, 2, 3, 0, 0 ], [ 0, 1, 2, 3, 3, 0, 2, 0 ], 
  [ 0, 1, 2, 3, 0, 3, 2, 0 ], [ 0, 1, 2, 3, 3, 0, 0, 2 ], 
  [ 0, 1, 2, 3, 0, 3, 0, 2 ] ] 

The good node sequences determine the Mullineux map (see GoodNodes GoodNodes and Mullineux Mullineux). This function requires the package ``specht'' (see RequirePackage).

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