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2 results

The critical exponent of the Arshon words
Dalia Krieger
Journal: RAIRO - Theoretical Informatics and Applications / Volume 44 / Issue 1 / January 2010
Published online by Cambridge University Press: 11 February 2010, pp. 139-150
Print publication: January 2010
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Generalizing the results of Thue (for n = 2) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1–67] and of Klepinin and Sukhanov (for n = 3) [Discrete Appl. Math. 114 (2001) 155–169], we prove that for all n ≥ 2, the critical exponent of the Arshon word of order n is given by (3n–2)/(2n–2), and this exponent is attained at position 1.

On Critical exponents in fixed points of k-uniform binary morphisms
Dalia Krieger
Journal: RAIRO - Theoretical Informatics and Applications / Volume 43 / Issue 1 / January 2009
Published online by Cambridge University Press: 20 December 2007, pp. 41-68
Print publication: January 2009
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Let w be an infinite fixed point of a binary k-uniform morphism f, and let Ew be the critical exponent of w. We give necessary and sufficient conditions for Ew to be bounded, and an explicit formula to compute it when it is. In particular, we show that Ew is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.