发表机构
Institut Camille Jordan, Université Claude Bernard Lyon 1（卡米尔·让研究所，里昂第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究从组合与拓扑视角分析作者提出的改进丢番图指数，证明三元字母表上其谱为[1,∞]，具刘维尔数集类拓扑性质，并给出多类无限字的具体示例。
AI 中文摘要
作者最近引入的改进丢番图指数是一种用于测量无限字周期性的量。本文从组合和拓扑视角研究该指数：首先，证明在三元字母表上，改进丢番图指数的谱为[1,∞]；其次，证明该指数具有与刘维尔数集类似的拓扑性质；最后，给出具体示例，包括Champernowne字、Rudin–Shapiro字、Thue–Morse字、通过区间旋转编码得到的字以及括号字。
英文摘要
The refined Diophantine exponent, recently introduced by the author, is a quantity that measures the periodicity of an infinite word. In this article, we study this exponent from combinatorial and topological viewpoints. First, we show that, over a ternary alphabet, the spectrum of the refined Diophantine exponent is $[1,\infty]$. Second, we show that this exponent has topological properties similar to those of the set of Liouville numbers. Finally, we provide concrete examples with the Champernowne, Rudin--Shapiro, and Thue--Morse words, words coming from coding a rotation by intervals, and bracket words.
CommentsReorganize the paper, fix the argument in Section 5, remove and add some questions
