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Robinson-Schensted-Knuth (RSK) correspondence is a bijective correspondencebetween two-rowed arrays of non-negative integers and pairs of same-shapesemistandard tableaux. This correspondence satisfies the symmetry property,that is, exchanging the rows of a two-rowed array is equivalent to exchangingthe positions of the corresponding pair of semistandard tableaux. In thisarticle, we introduce a super analogue of the RSK correspondence for supertableaux over a signed alphabet using a super version of Schensted's insertionalgorithms. We give a geometrical interpretation of the super-RSKcorrespondence by a matrix-ball construction, showing the symmetry property incomplete generality. We deduce a combinatorial version of the superLittlewood-Richardson rule on super Schur functions over a finite signedalphabet. Finally, we introduce the notion of super Littlewood-Richardson skewtableaux and we give another combinatorial interpretation of the superLittlewood-Richardson rule.

A super Robinson-Schensted-Knuth correspondence with symmetry and the super Littlewood-Richardson rule