| Issue |
RAIRO-Theor. Inf. Appl.
Volume 50, Number 1, January-March 2016
Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique"
|
|
|---|---|---|
| Page(s) | 21 - 38 | |
| DOI | https://doi.org/10.1051/ita/2016004 | |
| Published online | 02 June 2016 | |
An isolated point in the Heinis spectrum
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
turki@iml.univ-mrs.fr
Received:
24
March
2016
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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