The method used to compute the value of a character on a permutation is the recursion formula of Murnaghan and Nakayama [JK81, p. 60], except when computing the value of a character on the identity permutation a formula for the dimension of the representation indexed by a partition is used, [JK81, p. 56].
Computes the value of the irreducible character of the symmetric group of degree n indexed by the partition pa of weight n on the permutation pe. When computing the value of the character on the identity permutation, i.e. the degree of the character, the dimension (hook) formula is used on the partition pa.
Return the character of the representation of the symmetric group of degree n indexed by the partition pa where pa has weight n.
Return the character table of the symmetric group of degree d.