论文标题
通过无法区分的渐近对表征Sturmian序列的表征
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
论文作者
论文摘要
我们从难以区分的渐近对方面给出了生物芬太尼斯特里派序列的新表征。如果每个序列中的每个模式的出现集合至有限支持的置换量，则整个$ \ mathbb {z} $ - 移位上的两个渐近序列是无法区分的。这种特征可以看作是对基督教词语词的比里略定理的生物限定序列的扩展。此外，我们使用替换和生物限定特征性sturmian序列在任意字母上提供了不可区分的渐近对的完整表征。该证明是基于众所周知的衍生序列概念。
We give a new characterization of biinfinite Sturmian sequences in terms of indistinguishable asymptotic pairs. Two asymptotic sequences on a full $\mathbb{Z}$-shift are indistinguishable if the sets of occurrences of every pattern in each sequence coincide up to a finitely supported permutation. This characterization can be seen as an extension to biinfinite sequences of Pirillo's theorem which characterizes Christoffel words. Furthermore, we provide a full characterization of indistinguishable asymptotic pairs on arbitrary alphabets using substitutions and biinfinite characteristic Sturmian sequences. The proof is based on the well-known notion of derived sequences.
