= Dual Robinson–Schensted–Knuth correspondence
{title2=$M\longleftrightarrow(T,U),\quad T,U^t\text{ semistandard}$}
For a finite $0$-$1$ matrix, list its occupied pairs by increasing top entry and decreasing bottom entry within a top-entry tie. Perform ordinary semistandard <row insertion> on the bottom entries and record top entries in the new cells. The result is a <bijection> with same-shape tableaux $T,U$ for which $T$ and $U^t$ are <Semistandard Young tableaux>. The types of $T$ and $U$ are respectively the column-sum and row-sum vectors of the matrix.
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