= Frobenius alternant character formula
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{title2=$\chi^\lambda(\alpha)=[x^{\lambda+\delta}]\,p_\alpha(x)A_\delta(x)$}
For a <partition of an integer> $\lambda\vdash n$, padded to $m$ rows, let $\delta=(m-1,\ldots,0)$. If a permutation has $\alpha_q$ cycles of length $q$, put $p_\alpha=\prod_q(\sum_i x_i^q)^{\alpha_q}$. The <character> of the <Specht module> $S^\lambda$ is the displayed coefficient. Equivalently $p_\alpha A_\delta=\sum_\lambda\chi^\lambda(\alpha)A_{\lambda+\delta}$, the alternant form of the <Frobenius characteristic map>. It gives finite coefficient computations without constructing representation matrices.
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