A Generalization of Aztec Diamond Theorem, Part I

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.