[[Tensor representation]]
# Stanley's hook content formula

The number of [[Semi-standard Young tableau|semi-standard Young tableaux]] $\Theta$ of shape $\lambda$ with all $\Theta(i,j) \leq N$ is given by
$$
\begin{align*}
m_{\lambda}^N = \prod_{i,j \in \lambda} \frac{N - i + j}{h_{\lambda}(i,j)}
\end{align*}
$$
where $h_{\lambda}(i,j)$ is the [[Hook length]]. #m/thm/comb

> [!missing]- Proof
> #missing/proof Very complicated combinatorial proof



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