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» Tiling layouts with dominoes
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LATA
2009
Springer
14 years 2 months ago
Tiling the Plane with a Fixed Number of Polyominoes
Deciding whether a finite set of polyominoes tiles the plane is undecidable by reduction from the Domino problem. In this paper, we prove that the problem remains undecidable if t...
Nicolas Ollinger
TCS
2010
13 years 5 months ago
A hierarchical strongly aperiodic set of tiles in the hyperbolic plane
We give a new construction of strongly aperiodic set of tiles in H2 , exhibiting a kind of hierarchical structure, simplifying the central framework of Margenstern’s proof that t...
Chaim Goodman-Strauss
CORR
2007
Springer
149views Education» more  CORR 2007»
13 years 7 months ago
About the domino problem in the hyperbolic plane, a new solution
In this paper, we complete the construction of paper [9, 11]. Together with the proof contained in [9, 11], this paper definitely proves that the general problem of tiling the hy...
Maurice Margenstern
DLT
2008
13 years 8 months ago
Fixed Point and Aperiodic Tilings
An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics rangin...
Bruno Durand, Andrei E. Romashchenko, Alexander Sh...
JDA
2006
106views more  JDA 2006»
13 years 7 months ago
An optimal algorithm to generate tilings
We produce an algorithm that is optimal with respect to both space and execution time to generate all the lozenge (or domino) tilings of a hole-free, general-shape domain given as...
Sébastien Desreux, Eric Rémila