论文标题
$ \ MATHCAL {S} $ - 最小树状偏移的ADIC表征
$\mathcal{S}$-adic characterization of minimal dendric shifts
论文作者
论文摘要
树枝状转移是通过对语言中单词的扩展的组合限制来定义的。这个家族概括了众所周知的转变家庭，例如斯特里亚人的转变，arnoux-rauzy的转移和间隔交换转换的编码。众所周知，任何最小的树枝状移动都有一个原始的$ \ MATHCAL {s} $ - ADIC表示，其中$ \ Mathcal {S} $中的形态是Alphabet生成的免费组的正驯服自动形态。在本文中，我们通过两个有限图给出了$ \ Mathcal {s} $ - 该家族的ADIC表征。作为应用程序，我们能够决定（最终）dendric是由统一复发的形态词产生的变化空间。
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. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric.
