论文标题
Kolakoski序列：复发，对称性和极限密度之间的联系
Kolakoski Sequence: Links between Recurrence, Symmetry and Limit Density
论文作者
论文摘要
Kolakoski序列$ s $是$ \ weft \ lbrace 1,2 \ right \ rbrace^ω$的唯一元素，从1开始，并与其自身的运行长度编码相吻合。我们将$ s $的初始单词特定子类长度的均等作为统一工具，以解决主要开放问题之间的链接 - 复发，镜像/逆转不变性和数字的渐近密度。特别是我们证明复发意味着逆转不变性，并提供足够的条件，这意味着1s的密度为$ \ frac {1} {2} $。
The Kolakoski sequence $S$ is the unique element of $\left\lbrace 1,2 \right\rbrace^ω$ starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of $S$ as a unifying tool to address the links between the main open questions - recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is $\frac{1}{2}$.
