For n-cycles, Murnaghan–Nakayama gives a very simple computation of the irreducible character $\chi^{\lambda}_{(n)}$. However, computing the value on other pure cycles, even for something as simple as transpositions, seems much more complicated. Is there a nice formula for the character of these special cases?
2026-04-04 06:10:27.1775283027
Computing the irreducible characters of $S_n$ for cycles
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