An isolated point in the Heinis spectrum
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 21-38.

This paper continues the study initiated by Alex Heinis of the set H of pairs (α,β) obtained as the lower and upper limit of the ratio of complexity and length for an infinite word. Heinis proved that this set contains no point under a certain curve. We extend this result by proving that there are only three points on this curve, namely (1,1), (3/2, 5/3) and (2,2), and moreover the point (3/2, 5/3) is an isolated point in the set H. For this, we use Rauzy graphs, generalizing techniques of Ali Aberkane.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2016004
Classification : 68R15
Mots clés : Rauzy graph, Sturmian words, complexity function
Turki, Ramzi 1, 2

1 Institut de mathématiques de Marseille, Université d’Aix-Marseille, Case 907, 163, avenue de Luminy, 13288 Marseille, cedex 9, France
2 Faculté des Sciences de Sfax, Département de Mathématiques, Route de la Soukra km 3.5, B.P. 1171, 3000 Sfax, Tunisie
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Turki, Ramzi. An isolated point in the Heinis spectrum. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 1, pp. 21-38. doi : 10.1051/ita/2016004. http://archive.numdam.org/articles/10.1051/ita/2016004/

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