These methods describe the result of applying plethystic operations to a virtual character of a symmetric group. These operations are described either via a symmetric function f, or a partition lambda. Since cF corresponds to an S_n- representation, the option GroupActing is irrelevant in this case.
i1 : cF = new ClassFunction from {{2} => 1, {1,1} => -1};
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i2 : pl1 = plethysm({1,1},cF)
o2 = ClassFunction{{1, 1} => 1}
{2} => 1
o2 : ClassFunction
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i3 : R = symmetricRing 5; |
i4 : pl2 = plethysm(e_1+e_2,cF)
o4 = ClassFunction{{1, 1} => 0}
{2} => 2
o4 : ClassFunction
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i5 : S = schurRing R; |
i6 : symmetricFunction(cF,S)
o6 = -s
1,1
o6 : S
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i7 : symmetricFunction(pl1,S)
o7 = s
2
o7 : S
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i8 : symmetricFunction(pl2,S)
o8 = s - s
2 1,1
o8 : S
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