centralizerSize -- Size of the centralizer of a permutation

rho is a list representing the cycle type of some permutation: the i-th entry in rho is the number of cycles of length i of the permutation. The output of the function centralizerSize is the size of the centralizer in the symmetric group of any permutation of cycle type rho. The cycle type rho corresponds to a partition lambda, in which case centralizerSize(rho) is also the value of the square norm of the symmetric function p_{lambda}.

i1 : centralizerSize{1,1,1}

o1 = 6

i2 : R = symmetricRing(QQ,6);

i3 : u = p_1 * p_2 * p_3;

i4 : scalarProduct(u,u)

o4 = 6

o4 : QQ