= Littlewood–Richardson coefficient
{c}
{title2=$c_{\alpha\beta}^\nu$}
The nonnegative integer $c_{\alpha\beta}^\nu$ is the multiplicity of $S^\nu$ in $\operatorname{Ind}_{S_{|\alpha|}\times S_{|\beta|}}^{S_{|\nu|}}(S^\alpha\boxtimes S^\beta)$ in characteristic zero. The <Littlewood–Richardson rule> counts it by <Semistandard Young tableaux> of skew shape $\nu/\alpha$, content $\beta$, and <lattice word> in right-to-left, top-to-bottom reading order. For example $c_{(3,2,1),(3,2)}^{(5,3,2,1)}=3$: the two new top cells must be ones, and the remaining reading letters can be $122,212,221$. This coefficient also multiplies <Schur functions> in the <induction ring of symmetric-group characters>.
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