Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a permutation. The quiver formula of Buch and Fulton [BF] expresses these polynomials as an integer linear combination of products of Schur determinants. We present a positive, nonrecursive combinatorial formula for the coefficients. Our result is applied to obtain new expansions for the Schubert polynomials of Lascoux and Schützenberger [LS1] and explicit Giambelli formulas in the classical and quantum cohomology ring of any partial flag variety.
Anders S. Buch. Andrew Kresch. Harry Tamvakis. Alexander Yong. "Schubert polynomials and quiver formulas." Duke Math. J. 122 (1) 125 - 143, 15 March 2004. https://doi.org/10.1215/S0012-7094-04-12214-6