Vice-tableaux

The Robinson-Schensted construction associates a tableau with each word. The shape of that tableau is said to be plactic and may be regarded as a norm of the free monoid in the lattice of the partitions.

We give some properties on the products of the rows that are maximal with respect to the plactic form, the so-called franc words.

Among the franc words of a plactic class there exists one word that satisfies several properties of extremality, the so-called vice-bableau. With each plactic class of a permutation we can associate such a word which is also basic in the description of the Schubert polynomials by tableaux.