  Let $G$ be a classical complex Lie group, $P$ any parabolic subgroup of $G$,
and $G/P$ the corresponding partial flag variety. We prove an explicit
combinatorial Giambelli formula which expresses an arbitrary Schubert class in
the cohomology ring of $G/P$ as a polynomial in certain special Schubert class
generators. Our formula extends to one that applies to the torus-equivariant
cohomology ring of $G/P$ and to the setting of symplectic and orthogonal
degeneracy loci.
