Results 11 to 20 of about 33,813 (262)
Local Rules for Computable Planar Tilings [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Aperiodic tilings are non-periodic tilings characterized by local constraints. They play a key role in the proof of the undecidability of the domino problem (1964) and naturally model quasicrystals (discovered in 1982).
Thomas Fernique, Mathieu Sablik
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Bounded Wang tilings with integer programming and graph-based heuristics [PDF]
Scientific Reports, 2023 Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane.
Marek Tyburec, Jan Zeman
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Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile. [PDF]
Discrete Comput Geom, 2023 AbstractWe construct an example of a group$$G = \mathbb {Z}^2 \times G_0$$G=Z2×G0for a finite abelian group $$G_0$$G0, a subsetEof $$G_0$$G0, and two finite subsets$$F_1,F_2$$F1,F2of G, such that it is undecidable in ZFC whether$$\mathbb {Z}^2\times E$$Z2×Ecan be tiled by translations of$$F_1,F_2$$F1,F2.
Greenfeld R, Tao T.
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Generalized Dyck tilings (Extended Abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of
Matthieu Josuat-Vergès, Jang Soo Kim
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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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IEEE Access, 2021 Multiprimary displays reproduce colors by using combinations of four or more lights that are referred to as primaries. A display control vector defines the relative intensities of the primaries and determines the rendered color. For multiprimary displays,
Carlos Eduardo Rodriguez-Pardo +1 more
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Transactions of the American Mathematical Society, 2012 The authors consider the golden Anosov automorphism \(G_A\) on the torus \(\mathbb{T}^2\), defined in such a way that the ratio of its unstable and stable eigenvalues is the golden number \((1+ \sqrt 5)/2\). They study the space \({\mathcal G}\) of all \(C^{1 + \alpha}\) diffeomorphisms that are topologically conjugate to \(G_A\) and possess an ...
Pinto, Alberto A. +2 more
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The Electronic Journal of Combinatorics, 1996 Given a list $1\times 1, 1\times a, 1\times b, \dots, 1\times c$ of rectangles, with $a,b,\dots,c$ non-negative, when can $1\times{t}$ be tiled by positive and negative copies of rectangles which are similar (uniform scaling) to those in the list? We prove that such a tiling exists iff $t$ is in the field $Q(a,b,\dots,c)$.
Keating, Kevin, King, Jonathan L.
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Structure of spaces of rhombus tilings in the lexicograhic case [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Rhombus tilings are tilings of zonotopes with rhombohedra. We study a class of \emphlexicographic rhombus tilings of zonotopes, which are deduced from higher Bruhat orders relaxing the unitarity condition.
Éric Rémila
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Journal of Symbolic Logic, 2001 AbstractWe study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling withKolmogorov complexity of its (n×n)-squares. We construct tile sets for which this bound is tight: all (n×n)-squares in all tilings have complexity Ω(n).
Durand, Bruno +2 more
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