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Growth of Power-Free Languages over Large Alphabets

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Abstract

We study growth properties of power-free languages over finite alphabets. We consider the function α(k,β) whose values are the exponential growth rates of β-power-free languages over k-letter alphabets and clarify its asymptotic behaviour. Namely, we prove asymptotic formulas for this function for the case β≥2 and suggest such formulas for the case β<2 on the base of some partial results. All obtained formulas correlate very well with the known numerical bounds on the values of α(k,β).

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Notes

  1. Apart from the case a=n+s=k which is also consistent with the general pattern.

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  1. Ural Federal University, Ekaterinburg, Russia

    Arseny M. Shur

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  1. Arseny M. Shur
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Shur, A.M. Growth of Power-Free Languages over Large Alphabets. Theory Comput Syst 54, 224–243 (2014). https://doi.org/10.1007/s00224-013-9512-x

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