 Standard Young tableau

A standard Young tableau fills a Young diagram bijectively with $1,\dots ,n$, 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 $S^{\lambda }$.