2016/09/11 by Tri Lai, Lai, Tri
Engineering · Materials Science · Mathematics · #05A15 #05B45 #05C50 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1609.03116
openalex publication_date 2016/09/11 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28
We use the subgraph replacement method to investigate new properties of the\ntilings of regions on the square lattice with diagonals drawn in. In\nparticular, we show that the centrally symmetric tilings of a generalization of\nthe Aztec diamond are always enumerated by a simple product formula. This\nresult generalizes the previous work of Ciucu (1997) and Yang (1992) about\nsymmetric tilings of the Aztec diamond. We also use our method to prove a\nclosed-form product formula for the number of centrally symmetric tilings of a\nquasi-hexagon.\n