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Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai
Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai
Department of Mathematics: Faculty Publications
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.
A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai
A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai
Department of Mathematics: Faculty Publications
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas’ theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schr¨oder paths, then applying Lindstr¨om-Gessel-Viennot methodology.