Title: Skew Schubert Polynomials.
Session Name: Special Session on Algebraic Combinatorics

Author: Cristian Lenart
Author: Frank Sottile
Abstract:
We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. This definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in the Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. Lastly, we relate the construction of Bergeron and Sottile the construction of Schubert polynomials in terms of rc-graphs.