Balanced Fibonacci word rectangles, and beyond
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914495899631616 |
|---|---|
| author | Shallit, Jeffrey Vukusic, Ingrid |
| author_facet | Shallit, Jeffrey Vukusic, Ingrid |
| contents | Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to every Sturmian characteristic word corresponding to a quadratic irrational. Finally, we also examine the analogous question for the Tribonacci word and the Thue-Morse word. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Balanced Fibonacci word rectangles, and beyond Shallit, Jeffrey Vukusic, Ingrid Number Theory Discrete Mathematics Formal Languages and Automata Theory Combinatorics Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to every Sturmian characteristic word corresponding to a quadratic irrational. Finally, we also examine the analogous question for the Tribonacci word and the Thue-Morse word. |
| title | Balanced Fibonacci word rectangles, and beyond |
| topic | Number Theory Discrete Mathematics Formal Languages and Automata Theory Combinatorics |
| url | https://arxiv.org/abs/2509.25994 |