Ten Squares Force an Overlap
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918527965855744 |
|---|---|
| author | Shallit, Jeffrey |
| author_facet | Shallit, Jeffrey |
| contents | We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of squares. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28570 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ten Squares Force an Overlap Shallit, Jeffrey Combinatorics Discrete Mathematics Formal Languages and Automata Theory We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of squares. |
| title | Ten Squares Force an Overlap |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2605.28570 |