The Number of Threshold Words on n Letters Grows Exponentially for Every n≥ 27

11/13/2019

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by   James D. Currie, et al.

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For every n≥ 27, we show that the number of n/(n-1)^+-free words (i.e., threshold words) of length k on n letters grows exponentially in k. This settles all but finitely many cases of a conjecture of Ochem.