116 research outputs found
The finite tiling problem is undecidable in the hyperbolic plane
In this paper, we consider the finite tiling problem which was proved
undecidable in the Euclidean plane by Jarkko Kari in 1994. Here, we prove that
the same problem for the hyperbolic plane is also undecidable
Tiling Problems on Baumslag-Solitar groups
We exhibit a weakly aperiodic tile set for Baumslag-Solitar groups, and prove
that the domino problem is undecidable on these groups. A consequence of our
construction is the existence of an arecursive tile set on Baumslag-Solitar
groups.Comment: In Proceedings MCU 2013, arXiv:1309.104
About the domino problem in the hyperbolic plane from an algorithmic point of view
In this paper, we prove that the general problem of tiling the hyperbolic
plane with \`a la Wang tiles is undecidable.Comment: 11 pages, 6 figure
Constructing a uniform plane-filling path in the ternary heptagrid of the hyperbolic plane
In this paper, we distinguish two levels for the plane-filling property. We
consider a simple and a strong one. In this paper, we give the construction
which proves that the simple plane-filling property also holds for the
hyperbolic plane. The plane-filling property was established for the Euclidean
plane by J. Kari, in 1994, in the strong version
The domino problem on groups of polynomial growth
We characterize the virtually nilpotent finitely generated groups (or,
equivalently by Gromov's theorem, groups of polynomial growth) for which the
Domino Problem is decidable: These are the virtually free groups, i.e. finite
groups, and those having as a subgroup of finite index
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