RAIRO-Theor. Inf. Appl.
Volume 50, Number 1, January-March 2016Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique"
|Page(s)||21 - 38|
|Published online||02 June 2016|
An isolated point in the Heinis spectrum
Institut de mathématiques de Marseille, Université
d’Aix-Marseille, Case 907, 163,
avenue de Luminy, 13288
Marseille, cedex 9,
2 Faculté des Sciences de Sfax, Département de Mathématiques, Route de la Soukra km 3.5, B.P. 1171, 3000 Sfax, Tunisie
Accepted: 24 March 2016
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.
Mathematics Subject Classification: 68R15
Key words: Rauzy graph / Sturmian words / complexity function
© EDP Sciences 2016
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