The <Murnaghan–Nakayama rule> states that if a permutation has a $k$-cycle and remaining cycle type $\rho$, then
$$
\chi^\lambda(k,\rho)
=\sum_H(-1)^{\operatorname{leg}(H)}\chi^{\lambda\setminus H}(\rho),
$$
where $H$ runs over the removable <rim hook>[rim hooks] of length $k$. Iterating removes rim hooks whose lengths are the cycle lengths, and the character value is the signed sum over all complete removal sequences.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 160 / 2 / a / i / Solution

 Solution

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