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Results tagged with combinatorics-on-words
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user 12357
A branch of combinatorics that focuses on the study of words and formal languages
8
votes
Three-halves-free words (analogous to square-free)
This is not an answer, but it may help.
According to A generalization of repetition threshold by Lucian Iliea, Pascal Ochemb, and Jeffrey Shallit (Theoretical Computer Science, Volume 345, Issues 2–3 …
- 1,329
4
votes
4
answers
724
views
Subwords of cube-free binary words
I'm currently working on subwords of cube-free binary words.
A binary word is one composed of letters from a two-letter alphabet such as $\{0,1\}$. A word $y$ is a subword of $w$ if there exist word …
- 1,329
20
votes
4
answers
3k
views
Cube-free infinite binary words
A word $y$ is a subword of $w$ if there exist words $x$ and $z$ (possibly empty) such that $w=xyz$. Thus, $01$ is a subword of $0110$, but $00$ is not a subword of $0110$. I'm interested in right-in …
- 1,329
7
votes
Is it possible to create an infinite sequence in which no subsequence is repeated 3 times in...
For the question in the title, you're looking for cube-free infinite words. Of special interest are cube-free infinite words that are binary (use an alphabet of two letters). A lot of work has been …
- 1,329
4
votes
Concatenation of strings
Your question seems to be answered by Theorem 1.5.3 of Allouche and Shallit's Automatic Sequences: Theory, Applications, Generalizations (Cambridge University Press, 2003).
Let $x,y\in\Sigma^+$. …
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