Results 11 to 20 of about 6,397 (300)
Tilings by regular polygons—II A catalog of tilings [PDF]
, 1989 Several classification theorems involving highly symmetric tilings by regular polygons have been established recently. This paper surveys that work and gives drawings of these tilings—many of which were not shown in the original papers.
D. CHAVEY, Chavey, D.
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Transactions on Combinatorics, 2023 We 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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Spirals in Periodic Tilings [PDF]
, 2022 Spiral tilings, as appealing as they are for their aesthetics, have not been studied well mathematically. One of the difficulties in this area of tiling theory is providing a mathematical definition of spiral tilings.
Duero, Jessa Camille +2 more
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Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile [PDF]
Discrete & Computational Geometry, 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.
Rachel Greenfeld, Terence Tao
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Hexagonal Inflation Tilings and Planar Monotiles [PDF]
, 2012 Baake M, Gähler F, Grimm U. Hexagonal Inflation Tilings and Planar Monotiles. Symmetry. 2012;4(4):581-602.Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography.
Uwe Grimm +6 more
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CoRR, 2015 We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems -- we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.
Anne Kenyon, Martin Tassy
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Hard Tiling Problems with Simple Tiles [PDF]
Discrete & Computational Geometry, 2001 It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Satisfiability is NP-complete for planar cubic graphs.
Cristopher Moore, J. M. Robson
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The Mathematical Intelligencer, 2010 21 pages, 50 figures. Based on a Clay Public Lecture by the second author at the IAS/Park City Mathematics Institute in July, 2004.
Ardila, Federico, Stanley, Richard P.
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Elliptic Combinatorics and Markov Processes [PDF]
, 2012 We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the case of univariate functions, and Rains in the ...
Betea, Dan Dumitru
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European Journal of Combinatorics, 2021 25 pages, 5 figures; to appear in European Journal of ...
Jan Hladký, Ping Hu, Diana Piguet
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