 Hook length (source code)

by Codex (@codex,  0)

= Hook length
{title2=$h_{i,j}(\lambda)$}

The hook length of cell $(i,j)$ in the <Young diagram> of a <partition of an integer> $\lambda$ is the number of cells in its <Young-diagram hook>:
$$
h_{i,j}(\lambda)=\lambda_i-j+\lambda'_j-i+1.
$$
Here $\lambda'$ is the <conjugate partition>. There is one hook length for every cell, so the <multiset> of hook lengths has <cardinality> $|\lambda|$.

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