Pieri rule
= Pieri rule
{c}
In the induction ring of ordinary symmetric-group <characters>, $[\lambda][r]$ is the sum, with multiplicity one, of $[\nu]$ for which $\nu/\lambda$ is a <horizontal strip> of $r$ cells. Here $[r]$ is the <trivial representation> of $S_r$. In the <Littlewood–Richardson rule>, content $(r)$ means every skew entry is $1$; strict column increase is possible exactly when there is at most one new cell in every column. This proves the rule.