85 citations · 168 across the 13 of their papers we have counts for
6 papers · 1 filter
Domino Snake Problems on Groups
Nathalie Aubrun, Nicolas Bitar
In this article we study domino snake problems on finitely generated groups. We provide general properties of these problems and introduce new tools for their study. The first is t…
Strongly Aperiodic SFTs on Generalized Baumslag-Solitar groups
Nathalie Aubrun, Nicolás Bitar, Sacha Huriot-Tattegrain
We look at constructions of aperiodic SFTs on fundamental groups of graph of groups. In particular we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aper…
Row-constrained effective sets of colourings in the -fold horocyclic tessellations of are sofic
Nathalie Aubrun, Mathieu Sablik
In this article we prove that, restricted to the row-constrained case, effective sets of colourings in the -fold horocyclic tessellations of the hyperbolic plane …
Tiling Problems on Baumslag-Solitar groups
Nathalie Aubrun, Jarkko Kari
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 exist…
Multidimensional effective S-adic systems are sofic
Nathalie Aubrun, Mathieu Sablik
In this article we prove that multidimensional effective S-adic systems, obtained by applying an effective sequence of substitutions chosen among a finite set of substitutions, are…
An Order on Sets of Tilings Corresponding to an Order on Languages
Nathalie Aubrun, Mathieu Sablik
Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in t…