论文标题
在形态和斯特里式单词的扩展边界序列上
On extended boundary sequences of morphic and Sturmian words
论文作者
论文摘要
概括了陈和温引入的边界序列的概念，无限单词的$ \ ell $ boundary序列是有限的对$（u，v）$（u，v）的前缀和长度的后缀$ \ ell $ $ $ $ uyv $ uyv $ uyv $ uyv $ uyv $ u n+n+el e el ge（否则说，对于增加$ n $的值，一个人查看了由$ n- \ ell $符号分隔的所有长度$ \ ell $的所有对因素。 对于大型添加的抽象数字系统$ S $，我们表明，如果无限单词为$ s $ automatic，那么其$ \ ell $ bundary序列也相同。特别是它们既是形态（或由HD0L系统生成）。为了确保此结果的限制，我们讨论了不可起见的计算系统的示例和$ s $自动单词，但边界序列仍然是$ s $ sub-automatic，相反，$ s $ sub-autamic单词，其边界序列不是$ s $ $ autamic的。在本文的第二部分中，我们研究了sturmian单词的$ \ ell $ bundary序列。我们表明，它是通过同一斜率的特征性sturmian单词的滑动块代码获得的。我们还表明，这是在其他特征性的斯特里式单词的态度下的形象。
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the $n$th term of the $\ell$-boundary sequence of an infinite word is the finite set of pairs $(u,v)$ of prefixes and suffixes of length $\ell$ appearing in factors $uyv$ of length $n+\ell$ ($n\ge \ell\ge 1$). Otherwise stated, for increasing values of $n$, one looks for all pairs of factors of length $\ell$ separated by $n-\ell$ symbols. For the large class of addable abstract numeration systems $S$, we show that if an infinite word is $S$-automatic, then the same holds for its $\ell$-boundary sequence. In particular, they are both morphic (or generated by an HD0L system). To precise the limits of this result, we discuss examples of non-addable numeration systems and $S$-automatic words for which the boundary sequence is nevertheless $S$-automatic and conversely, $S$-automatic words with a boundary sequence that is not $S$-automatic. In the second part of the paper, we study the $\ell$-boundary sequence of a Sturmian word. We show that it is obtained through a sliding block code from the characteristic Sturmian word of the same slope. We also show that it is the image under a morphism of some other characteristic Sturmian word.
