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Bounded Wang tilings with integer programming and graph-based heuristics [PDF]
Scientific Reports, 2023 Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane.
Marek Tyburec, Jan Zeman
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Generalized Dyck tilings (Extended Abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of
Matthieu Josuat-Vergès, Jang Soo Kim
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Local Rules for Computable Planar Tilings [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Aperiodic tilings are non-periodic tilings characterized by local constraints. They play a key role in the proof of the undecidability of the domino problem (1964) and naturally model quasicrystals (discovered in 1982).
Thomas Fernique, Mathieu Sablik
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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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IEEE Access, 2021 Multiprimary displays reproduce colors by using combinations of four or more lights that are referred to as primaries. A display control vector defines the relative intensities of the primaries and determines the rendered color. For multiprimary displays,
Carlos Eduardo Rodriguez-Pardo +1 more
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Structure of spaces of rhombus tilings in the lexicograhic case [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Rhombus tilings are tilings of zonotopes with rhombohedra. We study a class of \emphlexicographic rhombus tilings of zonotopes, which are deduced from higher Bruhat orders relaxing the unitarity condition.
Éric Rémila
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Dyck tilings, linear extensions, descents, and inversions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths.
Jang Soo Kim +3 more
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Dihedral f-tilings of the sphere by rhombi and triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We classify, up to an isomorphism, the class of all dihedral f-tilings of S^2, whose prototiles are a spherical triangle and a spherical rhombus. The equiangular case was considered and classified in Ana M. Breda and Altino F.
Ana Breda, Altino F. Santos
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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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Recursive tilings and space-filling curves with little fragmentation
Journal of Computational Geometry, 2011 This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)).
Herman Haverkort
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