论文标题
隐藏的自动序列
Hidden automatic sequences
论文作者
论文摘要
自动序列是均匀形态的固定点的字母对字母编码。更普遍地，我们具有形态序列，它们是任意形态固定点的字母对字母编码。在许多示例中，一个具有\ emph {non-Corrifor}形态的先验，形态序列恰好是自动序列。一个例子是lysënok形态$ a \ to aca $，$ b \ to d $，$ c \ to b $，$ d \ to c $，其固定点也是2个自动序列。这种标识对于描述固定点生成的动力系统很有用。我们提供了几种方法来发现这种隐藏的自动序列，并提供了许多示例。我们特别关注与grigorchuk（类似）组相关的形态。
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where an, a priori, morphic sequence with a \emph{non-uniform} morphism happens to be an automatic sequence. An example is the Lysënok morphism $a \to aca$, $b \to d$, $c \to b$, $d \to c$, the fixed point of which is also a 2-automatic sequence. Such an identification is useful for the description of the dynamical systems generated by the fixed point. We give several ways to uncover such hidden automatic sequences, and present many examples. We focus in particular on morphisms associated with Grigorchuk(-like) groups.
