Standard Young tableau
= Standard Young tableau
{title2=$\operatorname{SYT}(\lambda)$}
A standard <Young tableau> fills a <Young diagram> bijectively with $1,\ldots,n$, increasing along rows and down columns. The cells occupied by the first $r$ entries form a diagram, so a tableau is equivalently a path formed by adjoining one <addable node of a Young diagram> at each step. The number of standard tableaux of shape $\lambda$ is the dimension of the complex <Specht module> $S^\lambda$.