The Number Of Threshold Words On N Letters Grows Exponentially For Every N >= 27

James D. Currie,Lucas Mol,Narad Rampersad

J. Integer Seq.（2020）

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摘要

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.

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关键词

threshold word,repetition threshold,Dejean word,exponential growth,Dejean's conjecture,Dejean's theorem

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