Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-Octagonal Regions
نویسنده
چکیده
We use the subgraph replacement method to prove a simple product formula for the tilings of an octagonal counterpart of Propp’s quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.
منابع مشابه
Alternating sign matrices and tilings of Aztec rectangles
The problem of counting numbers of tilings of certain regions has long interested researchers in a variety of disciplines. In recent years, many beautiful results have been obtained related to the enumeration of tilings of particular regions called Aztec diamonds. Problems currently under investigation include counting the tilings of related regions with holes and describing the behavior of ran...
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We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindström-GesselViennot methodology to find the number of tilings of a quartered lozenge hexagon.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016