Low complexity binary words avoiding $(5/2)^+$-powers
Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that...
Saved in:
| Published in | Discrete mathematics and theoretical computer science Vol. 27:3; no. Combinatorics |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
20.10.2025
|
| Online Access | Get full text |
| ISSN | 1365-8050 1462-7264 1365-8050 |
| DOI | 10.46298/dmtcs.15939 |
Cover
| Summary: | Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid $(5/2)^+$-powers, confirming a conjecture of Ollinger and Shallit.
12 pages; main structure theorem restated to cover all cases for complementation/reversal of factors |
|---|---|
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.15939 |