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12 votes
1 answer
682 views

A sum over characters of the symmetric group

Let $C_\mu$ be the size of the conjugacy class in $S_n$ of permutations whose cycletype is the partition $\mu\vdash n$. Let $\chi$ be the characters of the irreducible representations of $S_n$. Let $\...
thedude's user avatar
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11 votes
1 answer
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Probability of words summing to $1$ in $S_n$ or $\mathrm{PGL}_2(n)$

$\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Conj{Conj}$Let $G$ be the symmetric group $S_n$ or the projective general linear group $\PGL_2(n)$. Let $X$ be a cyclically reduced word in the ...
LeechLattice's user avatar
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