A Generalization of Aztec Diamond Theorem, Part I

Tri Lai

Abstract


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 Schröder paths, then applying Lindström-Gessel-Viennot methodology.


Keywords


Aztec diamonds, dominos, tilings, perfect matchings, Schröder paths

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