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

## Synopsis

• Function: plethysm
• Usage:
pl = plethysm(f,cF)
pl = plethysm(lambda,cF)
• Inputs:

## 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