有限指数基性质
The finite index basis property
摘要：
在本文中，我们描述了bifix码，符号动力系统和自由群之间的联系。这与先前为对应于斯特米亚语单词的符号系统建立的联系的精神是一致的。本文引入了一类具有线性因子复杂度的无限字的因子集，它包含Sturmian集和正则区间交换集，即树集类。作为主要结果，我们证明了对于一致递归树集$F$，字母表$A$上的有限bifix码$X$是$F$ -极大的$F$ -度$d$当且仅当它是$A$上自由群的指数$d$的子群的基.
英文摘要：
We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namemly the class of tree sets. We prove as a main result that for a uniformly recurrent tree set $F$, a finite bifix code $X$ on the alphabet $A$ is $F$-maximal of $F$-degree $d$ if and only if it is the basis of a subgroup of index $d$ of the free group on $A$.
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