  We give an explicit natural identification between the quiver coefficients of
Buch and Fulton, decomposition coefficients for Schubert polynomials, and the
Schubert structure constants for flag manifolds. This is also achieved in
K-theory where we give a direct argument that the decomposition coefficients
have alternating signs, based on a theorem of Brion, which then implies that
the quiver coefficients have alternating signs. Our identification shows that
known combinatorial formulas for the latter two numbers give formulas for the
quiver coefficients.
