= Power-sum border-strip multiplication
{title2=$p_rs_\mu=\sum_{\lambda/\mu\text{ rim hook of size }r}(-1)^{\operatorname{ht}(\lambda/\mu)}s_\lambda$}
Multiplication of an <alternant> by $p_r$ is the sum of alternants obtained by raising one row exponent by $r$. Equal exponents give zero. Otherwise sort the shifted <beta number of a partition> back into decreasing order. The resulting partition adds a size-$r$ <rim hook>; the number of crossed exponents is its height and supplies the <determinant> sign. This proves the formula through the <bialternant formula>. Iteration counts signed <border-strip tableaux>.
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