A Rewrite System Associated with Quadratic Pisot Units

@inproceedings{Frougny1999ARS,
  title={A Rewrite System Associated with Quadratic Pisot Units},
  author={Christiane Frougny and Jacques Sakarovitch},
  booktitle={RTA},
  year={1999}
}
In a previous work, we have investigated an automata-theoretic property of numeration systems associated with quadratic Pisot units that yields, for every such number θ, a certain group Gθ. In this paper, we characterize a cross-section of a congruence γθ ofZ4 that had arisen when constructing Gθ. In spite of the algebraic connections and implications of that characterization, the proof is combinatorial, and based upon rewriting techniques. The main point is to show that the rewrite… 
1 Citations

Two Groups Associated with Quadratic Pisot Units

TLDR
This paper characterize a cross-section of a congruence γθ of ℤ4 that had arisen when constructing Gθ, that becomes then a second group associated with θ, and is very similar to the symbolic dynamical system associated, by a theorem of Parry, with the two numeration systems attached to θ.

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