منابع مشابه
Enumeration of octagonal tilings
Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of the number of distinct tilings to the number of constituent tiles. Tilings by squares and 45 rhombi receive special attention as presumably the simplest mode...
متن کاملEnumeration of octagonal random tilings by the Gessel-Viennot method
We propose the first algebraic determinantal formula to enumerate random rhombus tilings filling a centro-symmetric octagon of any size. This result uses the GesselViennot technique and generalizes to any octagon a former specialized formula by Elnitsky.
متن کاملEnumeration of Hybrid Domino-Lozenge Tilings II: Quasi-Octagonal Regions
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.
متن کاملEnumeration of Tilings
Note: This survey article will be a chapter in the Handbook of Enumerative Com-binatorics, to be published by CRC Press in early 2015.
متن کاملInteger Groups of Coinvariants Associated to Octagonal Tilings
The integer groups of coinvariants associated to undecorated and decorated octagonal tilings are computed.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2015
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.03.019