For each $\alpha > 2$ there is an Infinite Binary Word with Critical Exponent $\alpha$

James D. Currie, Narad Rampersad


The critical exponent of an infinite word ${\bf w}$ is the supremum of all rational numbers $\alpha$ such that ${\bf w}$ contains an $\alpha$-power. We resolve an open question of Krieger and Shallit by showing that for each $\alpha > 2$ there is an infinite binary word with critical exponent $\alpha$.

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