Results 81 to 90 of about 33,997 (183)

Undecidability of Translational Tiling with Three Tiles

CoRR
Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by showing that an aperiodic monotile exists in sufficiently high dimension $n$ [Ann. Math. 200(2024), 301-363].
Chan Yang, Zhujun Zhang
openaire   +2 more sources

Ammann Bars for Octagonal Tilings [PDF]

Discrete Mathematics & Theoretical Computer Science
Ammann bars are formed by segments (decorations) on the tiles of a tiling such that forming straight lines with them while tiling forces non-periodicity.
Thomas Fernique, Carole Porrier
doaj   +1 more source

Tilings, sub-tilings, and spectral sets on p-adic space

Open Mathematics
In this article, we provide a characterization of tilings, sub-tilings, and spectral sets on the pp-adic space Qpd{{\mathbb{Q}}}_{p}^{d}. Our methods are based on pp-adic distributions and pp-adic Fourier analysis. We also obtained a sufficient condition
Kadir Mamateli
doaj   +1 more source

Quasicrystal Tilings in Three Dimensions and Their Empires

Crystals, 2018
The projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal’s vertex configurations, frequencies, and empires (forced tiles).
Dugan Hammock, Fang Fang, Klee Irwin
doaj   +1 more source

Combinatorial substitutions and sofic tilings

, 2010
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local constraints.
Fernique, Thomas, Ollinger, Nicolas
core   +2 more sources

Tilings with the Minimal Tile Property

, 2020
A square tiling of the unit square is said to have the minimal tile property if the smallest tile can tile all the other tiles. We show that in such a tiling, the smallest tile cannot be too small.
openaire   +2 more sources

Constructing a uniform plane-filling path in the ternary heptagrid of the hyperbolic plane [PDF]

Computer Science Journal of Moldova, 2007
In this paper, we distinguish two levels for the plane-filling property. We consider a simple and a strong one. In this paper, we give the construction which proves that the simple plane-filling property also holds for the hyperbolic plane.
Maurice Margenstern
doaj  

Classification and birational equivalence of dimer integrable systems for reflexive polygons

Journal of High Energy Physics
Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d 𝒩 = 1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds.
Minsung Kho, Norton Lee, Rak-Kyeong Seong   +2 more
doaj   +1 more source

Topological Boundary Floppy Modes in Quasicrystals

Physical Review X, 2019
Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices.
Di Zhou, Leyou Zhang, Xiaoming Mao
doaj   +1 more source

Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble

Forum of Mathematics, Pi
We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency location, converge ...
Amol Aggarwal, Jiaoyang Huang
doaj   +1 more source