Up to now, what are the difference ways we know to define RSK correspondence? I already know:


1. By insertion and recording tableau.
2. Ball construction or Viennot's geometric construction.
3. Growth diagram proposed by Sergey Fomin.


Do you know other models?



RSK correspondence
Here, slightly edited, is the first paragraph of Steinberg's paper, [An occurrence of the Robinson–Schensted correspondence](https://doi.org/10.1016/0021-8693(88)90177-9).



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> Let $V$ be an $n$-dimensional vector space over an infinite field, $\mathscr F$ the flag manifold of $V$, $u$ a unipotent transformation of $V$, and $\lambda$ the type of $u$, a partition of $n$ whose parts are the sizes of the Jordan blocks for $u$. … The components of $\mathscr F\_u$, the variety of flags fixed by $u$, correspond naturally to the standard tableaux of shape $\lambda$. The purpose of this note is to show that the "relative position" of any two components of $\mathscr F\_u$ (in general an element of the Weyl group, in the present case an element of $S\_n$) is given, in terms of the corresponding tableaux, by the Robinson–Schensted correspondence.
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