 Murnaghan–Nakayama rule

If a permutation has a $k$-cycle and remaining cycle type $\rho$, thenwhere the sum is over removable rim hooks of length $k$.

The Murnaghan–Nakayama rule is a tool used in representation theory, specifically in the context of symmetric functions and the study of representations of the symmetric group. This rule provides a method for calculating the characters of the symmetric group when restricted to certain subgroups, particularly the Young subgroups.