Murnaghan–Nakayama rule
= Murnaghan–Nakayama rule
{c}
{wiki}
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 $k$.