Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of two finite graphs.
翻译:语义变换由对其语言词语扩展的组合限制来定义。 这个家庭将众所周知的变换家庭, 如Sturmian 变换、 Arnoux- Rauzy 变换以及间隙交换转换的编码等, 已知任何最小的变换都有原始的 $mathcal{S}$- adi 表示, $\ mathcal{S} $的形态是字母制自由组的正式自体。 在本文中, 我们用两个限定图表来给出这个家庭的 $\ mathcal{S}$- a dic 描述 。