Skew Schubert functions and the Pieri formula for flag
manifolds
Nantel Bergeron and Frank Sottile
We show the equivalence of the Pieri formula for flag manifolds and
certain identities among the structure constants for the Schubert basis,
giving new proofs of both the Pieri formula and of these identities.
A key step is the association of a symmetric function to a finite
poset with labeled Hasse diagram satisfying a symmetry condition.
This gives a unified definition of skew Schur functions, Stanley
symmetric function, and skew Schubert functions (defined here).
We also use algebraic geometry to show the coefficient of a monomial in a
Schubert polynomial counts certain chains in the Bruhat order,
obtaining a new combinatorial construction of Schubert polynomials.
The manuscript in
postscript.
