Results 11 to 20 of about 29,883 (267)
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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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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, 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 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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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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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 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).
Bruno Durand 0001 +2 more
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