Murnaghan–Nakayama rule (source code)

= Murnaghan–Nakayama rule
{c}
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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 the sum is over removable rim hooks of length $k$.