= Row-column collision lemma
{title2=$\lambda\geq\mu\Longrightarrow\text{collision or }(\lambda=\mu,\ u=rct)$}
If the rows of a <Young tableau> of shape $\lambda$ have no repeated intersection with the columns of one of shape $\mu$, then $\sum_{i\leq k}\lambda_i\leq\sum_{i\leq k}\mu_i$ for every $k$. If also $\lambda\geq\mu$ in <dictionary order on integer partitions>, the shapes are equal. Saturation of the prefix bounds places one entry of each eligible row in each column, giving $u=rct$ with $r\in R(t)$ and $c\in C(t)$. A collision instead gives a <transposition> that makes row symmetrization followed by the relevant column antisymmetrization vanish.
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