Enumeration of Tilings of Quartered Aztec Rectangles

Tri Lai

Abstract


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 Lindström-Gessel-Viennot methodology to find the number of tilings of a quartered lozenge hexagon.

Keywords


Aztec diamonds, domino tilings, perfect matchings, quartered Aztec diamonds

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