71.8 Partitions in Specht

Many of the functions in Specht take partitions as arguments. Partitions are usually represented by lists in GAP. In Specht, all the functions which expect a partition will accept their argument either as a list or simply as a sequence of numbers. So, for example:

gap> H:=Specht(4);; H.S(H.P(6,4));
S(6,4)+S(6,3,1)+S(5,3,1,1)+S(3,3,2,1,1)+S(2,2,2,2,2)
gap> H.S(H.P([6,4]));
S(6,4)+S(6,3,1)+S(5,3,1,1)+S(3,3,2,1,1)+S(2,2,2,2,2) 

Some functions require more than one argument, but the convention still applies.

gap> ECore(3, [6,4,2]);
[ 6, 4, 2 ]
gap> ECore(3, 6,4,2);   
[ 6, 4, 2 ] 
gap> GoodNodes(3, 6,4,2);    
[ false, false, 3 ]
gap> GoodNodes(3, [6,4,2], 2);
3 

Basically, it never hurts to put the extra brackets in, and they can be omitted so long as this is not ambiguous. One function where the brackets are needed is DecompositionNumber; this is clear because the function takes two partitions as its arguments.

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