[[Young diagram]]
# Hook length

Given a [[Young diagram]] $\lambda$, the **hook** at $(i,j)$ is given by
$$
\begin{align*}
H_{\lambda}(i,j) = \{ (p,q) \in \lambda : p \geq i, q \geq j \}
\end{align*}
$$
and the hook length $h_{\lambda}(i,j)$ is the number of cells in $H_{\lambda}(i,j)$. #m/def/comb

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