If I want to obtain the
CycleIndexPolynomial of the symmetric group $S_n$, I can just do i.e.
x^4/24 + 1/4 x^2 x + x^2/8 + 1/3 x x + x/4
But what if I want to get the
CycleIndexPolynomial of the direct product of two symmetric groups $S_n\times S_m$? Which syntax should I use to obtain that? Or maybe there is some iterative way to get it? Thanks for any suggestion!
I know for a fact that the
CycleIndexPolynomial of $S_2\times S_2$ with all variables $x[i]$ evaluated at $x[i]=n$ should reduce to
n^4/4 + 3n^2/4
However, if we do
n^2/4 + n^3/2 + n^4/4
which is definitely not the same.