We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schub...

The quasisymmetric Macdonald polynomials G γ (X;q,t) were recently introduced by the first and second authors with Haglund, Mason, Williams in [3] to refine symmetric P λ property that (X;0,0) equals QS (X), Schur polynomial of [9]. We derive an expansion for fundamental basis functions.