Results 31 to 40 of about 6,397 (300)
Highly symmetric aperiodic structures -INVITED [PDF]
EPJ Web of Conferences, 2021 The symmetries of periodic structures are severely constrained by the crystallographic restriction. In particular, in two and three spatial dimensions, only rotational axes of order 1, 2, 3, 4 or 6 are possible.
Grimm Uwe
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The Crossing Number of The Hexagonal Graph H3,n
Discussiones Mathematicae Graph Theory, 2019 In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the ...
Wang Jing +2 more
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An n-Dimensional Generalization of the Rhombus Tiling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings,
Joakim Linde +2 more
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On the Notions of Symmetry and Aperiodicity for Delone Sets [PDF]
, 2012 Baake M, Grimm U. On the Notions of Symmetry and Aperiodicity for Delone Sets. Symmetry. 2012;4(4):566-580.Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the
Uwe Grimm +3 more
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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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, 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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International Journal of Mathematics and Mathematical Sciences, 1999 A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their pairwise-disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well ...
F. G. Arenas
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Examples and CounterexamplesTame SL2-tilings are related to Farey graph and friezes; much less is known about wild (not tame) SL2-tilings. In this note, we demonstrate SL2-tilings that are maximally wild: we prove that the maximum wild density of an integer SL2-tiling is 25 and ...
Andrei Zabolotskii
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Моделирование и анализ информационных систем, 2015 We study a problem about the number of lattice plane tilings by the given area centrosymmetrical polyominoes. A polyomino is a connected plane geomatric figure formed by joiining a finite number of unit squares edge to edge.
A. V. Shutov, E. V. Kolomeykina
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Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux +3 more
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