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On critical exponents in fixed points of $k$ -uniform binary morphisms

Dalia Krieger — 2009

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Let $𝐰$ be an infinite fixed point of a binary $k$ -uniform morphism $f$ , and let $E (𝐰)$ be the critical exponent of $𝐰$ . We give necessary and sufficient conditions for $E (𝐰)$ to be bounded, and an explicit formula to compute it when it is. In particular, we show that $E (𝐰)$ is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

The critical exponent of the Arshon words

Dalia Krieger — 2010

RAIRO - Theoretical Informatics and Applications

Generalizing the results of Thue (for ) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. (1912) 1–67] and of Klepinin and Sukhanov (for ) [Discrete Appl. Math. (2001) 155–169], we prove that for all ≥ 2, the critical exponent of the Arshon word of order is given by (3–2)/(2–2), and this exponent is attained at position 1.

On Critical exponents in fixed points of -uniform binary morphisms

Dalia Krieger — 2007

RAIRO - Theoretical Informatics and Applications

Let be an infinite fixed point of a binary -uniform morphism , and let be the critical exponent of . We give necessary and sufficient conditions for to be bounded, and an explicit formula to compute it when it is. In particular, we show that is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.