  In this paper, we continue the study of domino-tilings of Aztec diamonds. In
particular, we look at certain ways of placing ``barriers'' in the Aztec
diamond, with the constraint that no domino may cross a barrier. Remarkably,
the number of constrained tilings is independent of the placement of the
barriers. We do not know of a combinatorial explanation of this fact; our proof
uses the Jacobi-Trudi identity.
