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...
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...
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...
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...
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...