# Tiling Problems on Baumslag-Solitar groups

@inproceedings{Aubrun2013TilingPO, title={Tiling Problems on Baumslag-Solitar groups}, author={Nathalie Aubrun and Jarkko Kari}, booktitle={MCU}, year={2013} }

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.

## 33 Citations

Addendum to "Tilings problems on Baumslag-Solitar groups"

- MathematicsArXiv
- 2021

This addendum clarified the point that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for BS(m,n) given in the paper, and gave a detailed proof of the undecidability result.

Aperiodic Subshifts on Polycyclic Groups

- MathematicsArXiv
- 2015

We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].

The domino problem is undecidable on surface groups

- MathematicsMFCS
- 2019

It is shown that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property and applied to the fundamental group of any closed orientable surface of genus at least 2.

Strongly aperiodic subshifts on surface groups

- Mathematics
- 2015

We give strongly aperiodic subshifts of finite type on every hyperbolic surface group; more generally, for each pair of expansive primitive symbolic substitution systems with incommensurate growth…

The Domino Problem for Self-similar Structures

- MathematicsCiE
- 2016

The domino problem for tilings over self-similar structures of \(\mathbb {Z}^d\) given by forbidden patterns is defined and non-trivial families of subsets with decidable and undecidable Domino problem are exhibited.

Aperiodic subshifts of finite type on groups which are not finitely generated

- Mathematics
- 2022

We provide an example of a non-ﬁnitely generated group which admits a nonempty strongly aperiodic SFT. Furthermore, we completely characterize the groups with this property in terms of their ﬁnitely…

The domino problem on groups of polynomial growth

- Mathematics
- 2013

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…

A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings

- Mathematics
- 2020

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson.…

Some Notes about Subshifts on Groups

- MathematicsArXiv
- 2015

If a finitely presented group G admits a strongly aperiodic SFT, then G has decidable word problem, and this is true for the free group with 2 generators, Thompson's groups T and V, PSL2(Z) and any f.g. group of rational matrices which is bounded.

Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups

- MathematicsArXiv
- 2020

It is shown that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs, and that there exists a strongly a periodicity SFT on BS(n,n), which is similar to that presented by Aubrun and Kari.

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