Fibonacci、Thue-Morse 和 Rudin-Shapiro 词中的单色等差数列
Monochromatic arithmetic progressions in the Fibonacci, Thue-Morse, and Rudin-Shapiro words
AI总结：
本文研究 Fibonacci 词中固定公差最长单色等差数列的长度与位置，结合圆周旋转动力学与 Walnut 自动定理证明给出长度公式，并推广到 Thue-Morse 和 Rudin-Shapiro 词。
摘要：
我们研究 Fibonacci 词中固定公差的最长单色等差数列的长度和起始位置。我们用一个简单公式对其长度进行了完整分类。我们最强的结果是利用动力系统方法，特别是圆周旋转的动力学来证明的。我们还采用了基于计算机的方法，形式为自动定理证明软件 Walnut。这使我们能够扩展近期关于 Thue-Morse 词和 Rudin-Shapiro 词类似问题的结果。这也使我们能够获得 Fibonacci 词中一些似乎不适用于动力学方法的结果。
英文摘要：
We investigate the lengths and starting positions of the longest monochromatic arithmetic progressions for a fixed difference in the Fibonacci word. We provide a complete classification for their lengths in terms of a simple formula. Our strongest results are proved using methods from dynamical systems, especially the dynamics of circle rotations. We also employ computer-based methods in the form of the automatic theorem-proving software Walnut. This allows us to extend recent results concerning similar questions for the Thue-Morse word and the Rudin-Shapiro word. This also allows us to obtain some results for the Fibonacci word that do not seem to be amenable to dynamical methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
