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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.
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
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