For each a > 2 there is an Infinite Binary Word with Critical Exponent a
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Currie, James D.
Currie, James D., and Narad Rampersad. “For each a > 2 there is an Infinite Binary Word with Critical Exponent a.” Electronic Journal of Combinatorics 15(1) (2008): Note #N34.
The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite binary word with critical exponent α.