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\"{o}m-Gessel-Viennot methodology to find the number of tilings of a
quartered lozenge hexagon.Comment: 28 page
