Characterization of rational matrices that admit finite digit representations

@inproceedings{Jankauskas2018CharacterizationOR,
  title={Characterization of rational matrices that admit finite digit representations},
  author={Jonas Jankauskas and Jorg M. Thuswaldner},
  year={2018}
}
Let $A$ be an $n \times n$ matrix with rational entries and let \[ \mathbb{Z}^n[A] := \bigcup_{k=1}^{\infty} \left( \mathbb{Z}^n + A\mathbb{Z}^n + \dots + A^{k-1}\mathbb{Z}^n\right) \] be the minimal $A$-invariant $\mathbb{Z}$-module containing the lattice $\mathbb{Z}^n$. If $\mathcal{D}\subset\mathbb{Z}^n[A]$ is a finite set we call the pair $(A,\mathcal{D})$ a digit system. We say that $(A,\mathcal{D})$ has the finiteness property if each $\mathbf{z} \in \mathbb{Z}^n[A]$ can be written in the… CONTINUE READING
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