  K. Ding studied a class of Schubert varieties X_\lambda in type A partial
flag manifolds, corresponding to integer partitions \lambda and in bijection
with dominant permutations. He observed that the Schubert cell structure of
X_\lambda is indexed by maximal rook placements on the Ferrers board B_\lambda,
and that the integral cohomology groups H^*(X_\lambda; Zz), H^*(X_\mu; Zz) are
additively isomorphic exactly when the Ferrers boards B_\lambda, B_\mu satisfy
the combinatorial condition of rook-equivalence.
  We classify the varieties X_\lambda up to isomorphism, distinguishing them by
their graded cohomology rings with integer coefficients. The crux of our
approach is studying the nilpotence orders of linear forms in the cohomology
ring.
