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 simple combinatorial explanation of this fact: our proof uses the Jacobi Trudi identity.
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