论文标题
在忠实的斯特里派态度的代表
On a faithful representation of Sturmian morphisms
论文作者
论文摘要
将任何斯特里亚人序列映射到斯特里式序列的一组形态与所谓的sturm的单肌形成形成。对于这个monoid，我们以$（3 \ times 3）$ - 带有整数条目的矩阵来代表忠实的代表。我们在$ \ mathbb {r}^3 $中找到三个凸锥，并证明sl（\ mathbb {z}，3），3）中的矩阵$ r \是代表Sturmian形态的矩阵，如果三个锥体在$ r $ r $ r $ r $ r^{-1} $中不变。该属性提供了一种研究Sturmian序列的新工具。我们提供了由原始某些形态固定的Sturmian序列的四个已知结果的替代证明，以及有关Sturmian序列平方根的新结果。
The set of morphisms mapping any Sturmian sequence to a Sturmian sequence forms together with composition the so-called monoid of Sturm. For this monoid, we defne a faithful representation by $(3\times 3)$-matrices with integer entries. We find three convex cones in $\mathbb{R}^3$ and show that a matrix $R \in Sl(\mathbb{Z},3)$ is a matrix representing a Sturmian morphism if the three cones are invariant under multiplication by $R$ or $R^{-1}$. This property offers a new tool to study Sturmian sequences. We provide alternative proofs of four known results on Sturmian sequences fixed by a primitive morphism and a new result concerning the square root of a Sturmian sequence.
