Abstract
We extend the Robinson-Schensted-Knuth insertion procedure to tableaux over totally ordered sets and establish a correspondence from the set of monomials of certain types to the set of tableaux over totally ordered sets. It turns out that for the two dimensional case the said correspondence is bijective and for dimension greater than two, it is injective and the image of the set of monomials properly contain the set of standard tableaux. As a consequence we prove that the Straightening Law of Doubilet-Rota-Stein is not valid in the case of higher dimensional matrices.
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