Enumeration of Hybrid Domino-Lozenge Tilings III: Centrally Symmetric Tilings
arXiv:1609.03116
Abstract
We use the subgraph replacement method to investigate new properties of the tilings of regions on the square lattice with diagonals drawn in. In particular, we show that the centrally symmetric tilings of a generalization of the Aztec diamond are always enumerated by a simple product formula. This result generalizes the previous work of Ciucu (1997) and Yang (1992) about symmetric tilings of the Aztec diamond. We also use our method to prove a closed-form product formula for the number of centrally symmetric tilings of a quasi-hexagon.
arXiv comment33 pages and many figures. Accepted for publication in Australasian Journal of Combinatorics