论文标题
因子均衡$ S $ - 亚种语言
Factor-balanced $S$-adic languages
论文作者
论文摘要
如果每个字母的出现数量仅取决于单词的长度，则一组也称为语言，也称为字母平衡。同样，如果以相同长度有限的任何给定因素的发生数量的差异，则语言是均衡的。字母平衡但不是因子平衡语言的最突出的例子是Thue-Morse序列给出的。我们在两个概念之间建立了联系，特别是对于替换给出的语言，更普遍地是通过替换序列的语言。我们表明，当替换序列适当时，这两个概念基本上是重合的。以Thue-Morse-Sturmian语言为例，我们给出了因素平衡性的全部表征。
A set of words, also called a language, is letter-balanced if the number of occurrences of each letter only depends on the length of the word, up to a constant. Similarly, a language is factor-balanced if the difference of the number of occurrences of any given factor in words of the same length is bounded. The most prominent example of a letter-balanced but not factor-balanced language is given by the Thue-Morse sequence. We establish connections between the two notions, in particular for languages given by substitutions and, more generally, by sequences of substitutions. We show that the two notions essentially coincide when the sequence of substitutions is proper. For the example of Thue-Morse-Sturmian languages, we give a full characterisation of factor-balancedness.
