Questions tagged [symmetric-groups]

The symmetric group $S_n$ is the group of permutations of the set of integers ${1,\dots,n}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.

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sum of the character of the symmetric group

Suppose $\mu$ is a fixed partition of $n$ of length $l(\mu)$, and I was encountered with the following sum, namely $\sum_{\nu} \chi_{\nu}(\mu)$. I did some calculation using the character table that I can find (mainly Fulton & Harris's book, they…