Mathematics, Department of
Date of this Version
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.
the electronic journal of combinatorics 21(1) (2014), #P1.51