  The work of Buch and Fulton established a formula for a general kind of
degeneracy locus associated to an oriented quiver of type $A$. The main
ingredients in this formula are Schur determinants and certain integers, the
quiver coefficients, which generalize the classical Littlewood-Richardson
coefficients. Our aim in this paper is to prove a positive combinatorial
formula for the quiver coefficients when the rank conditions defining the
degeneracy locus are given by a permutation. In particular, this gives new
expansions for Fulton's universal Schubert polynomials and the Schubert
polynomials of Lascoux and Sch\"utzenberger.
