Beta set of a partition
= Beta set of a partition
{title2=$\beta(\lambda)$}
For $m\geq\ell(\lambda)$, a beta set is
$$
\{\lambda_i+m-i:1\leq i\leq m\}.
$$
A hook of length $h$ corresponds to a bead $b$ and an empty position $b-h$; removing the hook moves the bead to that gap.
= Beta set
{synonym}