THE RULE OF LITTLEWOOD-RICHARDSON IN A CONSTRUCTION OF BERENSTEIN-ZELEVINSKY

The rule of Littlewood-Richardson gives the decomposition of a product of Schur functions in the basis of the same functions. Each coefficient of this decomposition is the number of factorizations of a tableau of Yamanouchi in the plactic algebra. A. D. Berenstein and A. V. Zelevinksy prove that these coefficients are also the numbers of certain configurations called triangles. This text gives an explicit bijection between these triangles and the words of Yamanouchi.