On the growth rates of complexity of threshold languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 175-192.

Threshold languages, which are the (k/(k-1))+-free languages over k-letter alphabets with k ≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computer-assisted studies we conjecture that the growth rate of complexity of the threshold language over k letters tends to a constant α ^≈1.242 as k tends to infinity.

DOI : 10.1051/ita/2010012
Classification : 68Q70, 68R15
Mots-clés : power-free languages, Dejean's conjecture, threshold languages, combinatorial complexity, growth rate 
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Shur, Arseny M.; Gorbunova, Irina A. On the growth rates of complexity of threshold languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 175-192. doi : 10.1051/ita/2010012. http://www.numdam.org/articles/10.1051/ita/2010012/

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