A combinatorial construction of the Schubert polynomials

AbstractWe show a combinatorial rule based on diagrams (finite nonempty sets of lattice points (i, j) in the positive quadrant) for the construction of the Schubert polynomials. In the particular case where the Schubert polynomial is a Schur function we give a bijection between our diagrams and column strict tableaux. A different algorithm had been conjectured (and proved in the case of vexillary permutations) by A. Kohnert (Ph.D. dissertation, Universität auf Bayreuth, 1990). We give, at the end of this paper, a sketch of how one would show the equivalence of the two rules