Bibliographic Details
| Title: |
Monochromatic arithmetic progressions in the Fibonacci, Thue–Morse, and Rudin–Shapiro words. |
| Authors: |
Joshi, G.1 (AUTHOR) gandhar.joshi@open.ac.uk, Rust, D.1 (AUTHOR) dan.rust@open.ac.uk |
| Source: |
Theoretical Computer Science. Sep2025, Vol. 1050, pN.PAG-N.PAG. 1p. |
| Subjects: |
Arithmetic series, Dynamical systems, Number systems, Walnut, Rotational motion |
| Abstract: |
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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
