A note on antichains of words.
There are ternary circular square-free words of length for 18.
There exist binary circular power free words of every length.
Non-repetitive tilings.
For each there is an infinite binary word with critical exponent .
The number of ternary words avoiding abelian cubes grows exponentially.
Least periods of factors of infinite words
We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of sturmian words.
Least Periods of Factors of Infinite Words
We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of Sturmian words.
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