Results 11 to 20 of about 33,997 (183)
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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Tilings, tiling spaces and topology [PDF]
Philosophical Magazine, 2018 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.
Anderson JE +15 more
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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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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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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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, 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 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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The Estimation of the Number of Lattice Tilings of a Plane by a Given Area Polyomino
Моделирование и анализ информационных систем, 2013 We study a problem of a number of lattice plane tilings by given area polyominoes. A polyomino is a connected plane geometric figure formed by joining edge to edge a finite number of unit squares.
A. V. Shutov, E. V. Kolomeykina
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, 2014 Tiling is a well-known pattern mining technique. Traditionally, it discovers large areas of ones in binary databases or matrices, where an area is defined by a set of rows and a set of columns. In this paper, we introduce the novel problem of ranked tiling, which is concerned with finding interesting areas in ranked data. In this data, each transaction
Le Van, Thanh +5 more
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The Many Faces of Alternating-Sign Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles ...
James Propp
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