Specht and Hodge have shown that the space generated by products of minors of a matrix admits a linear basis in bijection with Young tableaux. The decomposition of any element into this basis is called straightening and corresponds to the iterative use of Plücker relations. Thanks to a well-known isomorphism between the space of harmonic polynomials and the space of polynomials modulo the ideal generated by symmetric polynomials, we can now use as a main technical tool the canonical scalar product on this later space. This leads to a different, and possibly better, algorithm for straightening.
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.
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