Inversions Tableaux

Abstract: We introduce inversions tableaux, a new combinatorial model for Schubert polynomials and Stanley-symmetric that directly specialize to semi-standard Young tableaux in the Grassmannian case. They are a modification of the balanced staircase tableaux of Edelman and Greene. We explicitly describe inversions tableaux that correspond to the lexicographically minimal and maximal monomials in each Schubert polynomial and characterize the unique inversions tableau for dominant permutations. We also define tableaux skew Schubert polynomials $\mathfrak{S}^t_{w/u}$ and prove certain properties about them.