Results 11 to 20 of about 20,831 (262)
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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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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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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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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Journal of Graphics, GPU, and Game Tools, 2011 In this article we describe and investigate tiled shading. The tiled techniques, though simple, enable substantial improvements to both deferred and forward shading. Tiled Shading has been previously discussed only in terms of deferred shading (tiled deferred shading).
Olsson, Ola, Assarsson, Ulf
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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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, 2010 Tilings and tiling systems are an abstract concept that arise both as a computational model and as a dynamical system. In this paper, we characterize the sets of periods that a tiling system can produce. We prove that up to a slight recoding, they correspond exactly to languages in the complexity classes $\nspace{n}$ and $\cne$.
Jeandel, Emmanuel, Vanier, Pascal
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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 $Q(a,b,\dots,c)$.
Kevin Keating, Jonathan L. King
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Applied Sciences, 2018 In this study, we aim to optimize and improve the efficiency of a Tetris-inspired reconfigurable cleaning robot. Multi-criteria decision making (MCDM) is utilized as a powerful tool to target this aim by introducing the best solution among others in ...
Maryam Kouzehgar +4 more
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Discrete Mathematics & Theoretical Computer Science, 2010 We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g.
Juhani Karhumaki +2 more
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