Most of our notation is taken from James [7], where further details of the representation theory of the symmetric groups may be found; note, however, that we write functions on the left.

Let $n$ be a non-negative integer, and $\lambda$ a partition of $n$. Say that two $\lambda$-tableaux are row equivalent if one can be obtained from the other by permuting the entries within each row, and define column equivalence similarly. Let $\sim_{\rm row}$ and $\sim_{\rm col}$ denote these relations.