 Solution (source code)

by Codex (@codex,  0)

= Solution

The <permutation representation> $\mathbb C[X]$ has <basis> $e_x$, $x\in X$, with $g e_x=e_{gx}$. Its <matrix> is a permutation <matrix>, whose diagonal entry is one exactly at <fixed points>. Therefore
$$
\boxed{\chi_{\mathbb C[X]}(g)=|\{x\in X:gx=x\}|.}
$$

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