Sturmian序列的不可区分渐近对刻画
A characterization of Sturmian sequences by indistinguishable asymptotic pairs
摘要：
利用不可区分渐近对给出了双无限Sturmian序列的一个新刻画。如果两个渐近序列中每个模式的出现集在每个序列中直到一个最小支持置换都重合，则在一个全$\mathbb{Z}$ -移位上的两个渐近序列是不可区分的。这个刻画可以看作是对描述Christoffel词的Pirillo定理的双无穷序列的扩展。此外，我们提供了一个完整的表征不可区分的渐近对任意字母表使用替换和双无限的特征Sturmian序列。证明是基于众所周知的概念派生序列。
英文摘要：
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.
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