In mathematics, Viennot's geometric construction (named after Xavier Gérard Viennot) gives a diagrammatic interpretation of the Robinson–Schensted correspondence in terms of shadow lines.
, written in two-line notation, say: one can apply the Robinson–Schensted correspondence to this permutation, yielding two standard Young tableaux of the same shape, P and Q. P is obtained by performing a sequence of insertions, and Q is the recording tableau, indicating in which order the boxes were filled.
Viennot's construction starts by plotting the points
in the plane, and imagining there is a light that shines from the origin, casting shadows straight up and to the right.
Removing these points and repeating the procedure, one obtains all the shadow lines for this permutation.
Viennot's insight is then that these shadow lines read off the first rows of P and Q (in fact, even more than that; these shadow lines form a "timeline", indicating which elements formed the first rows of P and Q after the successive insertions).
One can then repeat the construction, using as new points the previous unlabelled corners, which allows to read off the other rows of P and Q.