A Generalization of Aztec Dragons

Abstract

Aztec dragons are lattice regions first introduced by James Propp, which have the number of tilings given by a power of $2$. This family of regions has been investigated further by a number of authors. In this paper, we consider a generalization of the Aztec dragons to two new families of $6$-sided regions. By using Kuo's graphical condensation method, we prove that the tilings of the new regions are always enumerated by powers of $2$ and $3$.