Results 11 to 20 of about 6,990 (214)
Global dependences in hexagonal tiling
Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2020 Tiling is a widely used technique to solve the problems of the efficient use of multilevel memory and optimize data exchanges when developing both sequential and parallel programs. This paper investigates the problem of obtaining global dependencies, i.e. informational dependencies between tiles.
P. I. Sobolevsky +1 more
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A Periodic Hexagon Tiling Model and Non-Hermitian Orthogonal Polynomials [PDF]
Communications in Mathematical Physics, 2020 AbstractWe study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the asymptotic behavior can be separated into two regimes: the low and the high temperature regime.
C. Charlier +3 more
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Hybrid Hexagonal/Classical Tiling for GPUs [PDF]
Proceedings of Annual IEEE/ACM International Symposium on Code Generation and Optimization, 2014 Time-tiling is necessary for the efficient execution of iterative stencil computations. Classical hyper-rectangular tiles cannot be used due to the combination of backward and forward dependences along space dimensions. Existing techniques trade temporal data reuse for inefficiencies in other areas, such as load imbalance, redundant computations, or ...
Tobias Grosser +4 more
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Tilings of a Domain on a Hexagon Mesh with Balanced 3-Tiles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this article, we study the question of tilings on a hexagon mesh with balanced 3-tiles. This problem has been studied by Conway and Lagarias in [CL90], by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley graphs. We will use two different approaches.
Gilles Radenne
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A Double Tiling of Triangles and Regular Hexagons [PDF]
Discrete & Computational Geometry, 2000 Given a regular hexagon and a triangle both having a common edge, there exists a ring of five extra triangles each sharing an edge with the hexagon, as well as a ring of regular hexagons surrounding the triangles and having two edges in common with two successive triangles.
Hiroshi Okumura, J. F. Rigby
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Enumeration of lozenge tilings of hexagons with cut off corners [PDF]
Journal of Combinatorial Theory, Series A, 2001 23 pages, AmS ...
Mihai Ciucu, Christian Krattenthaler
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Right-Angled Hexagon Tilings of the Hyperbolic Plane [PDF]
, 2019 We study isometry-invariant probability measures on the space $ $ of tilings of the hyperbolic plane with right-angled hexagons of varying shapes. We prove that, for each measure $ $ in a certain natural family of measures on right-angled hexagons, there is an isometry-invariant measure on $ $ whose marginal distribution on tiles is $ $.
Richard Kenyon
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Hexagonal Tiling of the Plane [PDF]
Since the thesis of K. Reinhardt in 1918, it is well known that there are exactly three types of convex hexagons that can tile the plane. However, the proof of the fact is far from being complete. We prove this fact, under an assumption much weaker than the convexity.
Z. A. Zhu, Erxiao Wang, Min Yan
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Lozenge tilings of a hexagon and q-Racah ensembles
Journal of Physics A: Mathematical and TheoreticalAbstract We study the limiting behavior of random lozenge tilings of the hexagon with a q-Racah weight as the size of the hexagon grows large. Based on the asymptotic behavior of the recurrence coefficients of the q-Racah polynomials, we give a new proof for the fact that the height function for a random tiling concentrates near a ...
Maurice Duits, Erik Duse, Wenkui Liu
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Tiling Generating Functions of Halved Hexagons and Quartered Hexagons [PDF]
Annals of Combinatorics, 2021 We prove exact product formulas for the tiling generating functions of various halved hexagons and quartered hexagons with defects on boundary. Our results generalize the previous work of the first author and the work of Ciucu.
Lai, Tri, Rohatgi, Ranjan
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