71.39 EResidueDiagram

EResidueDiagram(H|e, mu)
EResidueDiagram(x)

The e--residue of the (i,j)--th node in the diagram of a partition mu is (j-i)bmod <e>. EResidueDiagram(e, mu) prints the diagram of the partition mu replacing each node with its e-residue.

If x is a module then EResidueDiagram(x) prints the e--residue diagrams of all of the e--regular partitions appearing in x (such diagrams are useful when trying to decide how to restrict and induce modules and also in applying results such as the ``Scattering theorem'' of [JM1]). It is not necessary to supply the integer e in this case because x ``knows'' the value of e.

gap> H:=Specht(2);; EResidueDiagram(H.S(H.P(7,5)));
[ 7, 5 ]
   0   1   0   1   0   1   0
   1   0   1   0   1
[ 6, 5, 1 ]
   0   1   0   1   0   1
   1   0   1   0   1
   0
[ 5, 4, 2, 1 ]
   0   1   0   1   0
   1   0   1   0
   0   1
   1
# There are 3 2-regular partitions.

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

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