We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr¨om-Gessel-Viennot methodology to find the number of tilings of a quartered lozenge hexagon.
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- Aztec diamonds
- Domino tilings
- Perfect matchings
- Quartered Aztec diamonds