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user 73667
For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.
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Two versions of the Murnaghan-Nakayama rule
I have always see the following Murnaghan-Nakayama rule for a partition $\lambda$ and a permutation $\sigma \in \mathfrak{S}_n$ of cycle structure $(\sigma_1, ..., \sigma_n)$:
$$
\chi_{\lambda}(\sigma …
- 891
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Closed formulas for the character of the symmetric group
I know the Murnaghan–Nakayama rule, but I am wondering if there is any closed formulas for the character of the symmetric group. I know the following:
$$\chi_{n}(\sigma) = 1$$
$$\chi_{11...1}(\sigma) …
- 50.8k