An isolated point in the Heinis spectrum

Turki, Ramzi

doi:10.1051/ita/2016004

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

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 21-38.

Résumé

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 : 2016-03-24
Accepté le : 2016-03-24

MR Zbl

DOI : 10.1051/ita/2016004

Classification : 68R15
Mots-clés : Rauzy graph, Sturmian words, complexity function

Affiliations des auteurs :

Turki, Ramzi ^{1, 2}

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     title = {An isolated point in the {Heinis} spectrum},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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     publisher = {EDP-Sciences},
     volume = {50},
     number = {1},
     year = {2016},
     doi = {10.1051/ita/2016004},
     mrnumber = {3518157},
     zbl = {1354.68218},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita/2016004/}
}

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Turki, Ramzi. An isolated point in the Heinis spectrum. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 21-38. doi : 10.1051/ita/2016004. https://www.numdam.org/articles/10.1051/ita/2016004/

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