关于无限可去替换词集
On sets of indefinitely desubstitutable words
摘要：
与给定的非擦除自同态或置换的集合S相关联的稳定集是S上所有可以无限去置换的右无限词的集合。这个概念推广了态射的不动点集的概念。它与S-adicity和保性质态射有关。考虑了两个主要问题。哪些已知的无限词集合是稳定集合？哪些是有限置换集的稳定集？在回答上述问题的同时，对一些著名的词集合，如二元平衡词集合和episturmian词集合，给出了一些新的刻画。还提供了一套nonerasing自同态，保持episturmian字的表征。
英文摘要：
The stable set associated to a given set S of nonerasing endomorphisms or substitutions is the set of all right infinite words that can be indefinitely desubstituted over S. This notion generalizes the notion of sets of fixed points of morphisms. It is linked to S-adicity and to property preserving morphisms. Two main questions are considered. Which known sets of infinite words are stable sets? Which ones are stable sets of a finite set of substitutions? While bringing answers to the previous questions, some new characterizations of several well-known sets of words such as the set of binary balanced words or the set of episturmian words are presented. A characterization of the set of nonerasing endomorphisms that preserve episturmian words is also provided.
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