Results 71 to 80 of about 33,813 (262)
Comptes Rendus. MathématiqueWe present a technique to lift some tilings of the discrete hyperbolic plane –tilings defined by a 1D substitution– into a zero entropy subshift of finite type (SFT) on non-abelian amenable groups $\mathit{BS}(1,n)$ for $n\ge 2$.
Aubrun, Nathalie, Schraudner, Michael
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Transactions on CombinatoricsWe provide a complete description of the edge-to-edge tilings with a regular triangle and a shield-shaped hexagon with no right angle. The case of a hexagon with a right angle is also briefly discussed.
Thomas Fernique, Olga Sizova
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Tilings, tiling spaces and topology [PDF]
Philosophical Magazine, 2006 To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk ...
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Rhombic tilings and Bott-Samelson varieties
, 2016 S.~Elnitsky (1997) gave an elegant bijection between rhombic tilings of $2n$-gons and commutation classes of reduced words in the symmetric group on $n$ letters.
Escobar, Laura +3 more
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Advanced Functional Materials, EarlyView.A previously unreported coordination motif stabilising single Fe atoms by indigo chelation and pyridyl coordination on Au(111) has been revealed. By using planar tritopic pyridyl linkers (TPyB), extended 2D porous networks of indigo3(TPyB)2Fe6 form. These networks can be crystalline or vitreous and offer an environment where individual coordination ...
Hongxiang Xu +9 more
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Classical Dimers on Penrose Tilings
Physical Review X, 2020 We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified as those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings).
Felix Flicker +2 more
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Annals of Combinatorics, 2010 This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the "tiles" have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods.
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C*-algebras of Penrose's hyperbolic tilings [PDF]
, 2010 Penrose hyperbolic tilings are tilings of the hyperbolic plane which admit, up to affine transformations a finite number of prototiles. In this paper, we give a complete description of the C*-algebras and of the K-theory for such tilings.
Oyono-Oyono, Hervé, Petite, Samuel
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Advanced Functional Materials, EarlyView.Guided by the golden ratio, a class of aperiodic architected metamaterials is introduced to address the intrinsic trade‐off between strength and toughness. By unifying local geometric heterogeneity with global order, the golden‐ratio‐guided aperiodic architecture promotes spatial delocalization of damage tolerence regions, leading to more tortuous ...
Junjie Deng +9 more
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Metaheuristic generation of brane tilings
Physics Letters BThe combinatorics of dimer models on brane tilings describe a large class of four-dimensional N=1 gauge theories that afford quiver descriptions and have toric moduli spaces. We introduce a combinatorial optimization method leveraging simulated annealing
Yang-Hui He +2 more
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