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 $H$ ranges over removable <rim hook>[rim hooks] of length $k$ and $\operatorname{leg}(H)$ is one less than the number of rows occupied by $H$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 160 / 2 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-160/2/b/i/solution