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Domino Tilings for Augmented Aztec Rectangles and Their Chains

Domino Tilings for Augmented Aztec Rectangles and Their Chains

Much work has been done to count the number of domino tilings for Aztec diamonds and augmented Aztec diamonds. Augmented Aztec rectangles and their chains are generalizations of these shapes. In this paper, we use Delannoy paths to count the number of domino tilings for these rectangles and their chains.