Past exam of the Lie algebras and representation theory of symmetric groups course of the University of Oxford / 2008 / B / 6 / a / Solution

If the cycle partition contains a part $r$, the Murnaghan–Nakayama rule isA border strip is a connected skew Young diagram with no $2\times 2$ block; its height is its number of occupied rows minus one. The remaining boxes must be a partition diagram. The recursion starts with character one for the empty diagram at the empty cycle type, and an empty sum is zero. Repeated removal for all cycle lengths computes the character value.