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SchurRings :: plethysm(RingElement,ClassFunction)

plethysm(RingElement,ClassFunction) -- Plethystic operations on class functions

Synopsis

Description

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};
i2 : pl1 = plethysm({1,1},cF)

o2 = ClassFunction{{1, 1} => 1}
                   {2} => 1

o2 : ClassFunction
i3 : R = symmetricRing 5;
i4 : pl2 = plethysm(e_1+e_2,cF)

o4 = ClassFunction{{1, 1} => 0}
                   {2} => 2

o4 : ClassFunction
i5 : S = schurRing R;
i6 : symmetricFunction(cF,S)

o6 = -s
       1,1

o6 : S
i7 : symmetricFunction(pl1,S)

o7 = s
      2

o7 : S
i8 : symmetricFunction(pl2,S)

o8 = s  - s
      2    1,1

o8 : S