= Beta number of a partition
{title2=$\beta_i=\lambda_i+l-i$}
= Beta number
{synonym}
= Beta numbers of a partition
{synonym}
For a partition padded to $l$ rows, its <beta numbers> are the distinct nonnegative integers $\lambda_i+l-i$. They are its occupied <abacus of a partition> positions. With exactly the positive row count, they equal the first-column <hook lengths>; extra zero rows change the <representation> of the <beta set> while preserving the partition. Individual <beta numbers> describe bead positions, whereas the <beta set> is the collection of all these numbers.
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