关于导子闭的Sturmian代换
On Sturmian substitutions closed under derivation
摘要：
因子$w$在无限均匀递归序列${\bf u}$中的出现可以由有限字母表上的无穷序列编码。该序列通常表示为${\bf d_{\bf u}}(w)$，并在${\bf u}$中称为$w$的衍生序列。如果$w$是本原置换$φ$的定点${\bf u}$的前缀，则根据Durand 1998年的结果，导出序列${\bf d_{\bf u}}(w)$也由本原置换$ψ$固定。对于非前缀因子$w$，导出序列${\bf d_{\bf u}}(w)$仅在例外情况下通过替换来固定。为了研究这一现象，我们引入了一个新的概念：有限置换集$M $称为导子闭集，如果导出序列${\bf d_{\bf u}}(w)$到$φ\in M$的任何不动点${\bf u}$的任何因子$w$由态射$ψ\in M$固定.在本文中，我们刻画了属于导子闭集$M$的Sturmian置换.特征化使用其不动点的斜率和截距或其S-adic表示。
英文摘要：
Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${\bf u}$ can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${\bf d_{\bf u}}(w)$ and called the derived sequence to $w$ in ${\bf u}$. If $w$ is a prefix of a fixed point ${\bf u}$ of a primitive substitution $φ$, then by Durand's result from 1998, the derived sequence ${\bf d_{\bf u}}(w)$ is fixed by a primitive substitution $ψ$ as well. For a non-prefix factor $w$, the derived sequence ${\bf d_{\bf u}}(w)$ is fixed by a substitution only exceptionally. To study this phenomenon we introduce a new notion: A finite set $M $ of substitutions is said to be closed under derivation if the derived sequence ${\bf d_{\bf u}}(w)$ to any factor $w$ of any fixed point ${\bf u}$ of $φ\in M$ is fixed by a morphism $ψ\in M$. In our article we characterize the Sturmian substitutions which belong to a set $M$ closed under derivation. The characterization uses either the slope and the intercept of its fixed point or its S-adic representation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
