Geodesic
On the Multivariate Robinson-Schensted Correspondence
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 591-602.

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We show the existence of a multivariate extension of the Robinson-Schensted correspondence. This is inspired by the interpretation of the classical two dimensional case in the invariant theory of (finite) reflection groups. 
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Caselli, Fabrizio. On the Multivariate Robinson-Schensted Correspondence. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 591-602. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a3/

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