scholarly journals A characterization of Sturmian sequences by indistinguishable asymptotic pairs

2021 ◽  
Vol 95 ◽  
pp. 103318
Author(s):  
Sebastián Barbieri ◽  
Sébastien Labbé ◽  
Štěpán Starosta
Keyword(s):  
Sturmian Sequences

scholarly journals Powers in Sturmian sequences

2003 ◽  
Vol 24 (4) ◽  
pp. 377-390 ◽  
Author(s):  
David Damanik ◽  
Daniel Lenz
Keyword(s):  
Sturmian Sequences

scholarly journals Initial powers of Sturmian sequences

2006 ◽  
Vol 122 (4) ◽  
pp. 315-347 ◽  
Author(s):  
Valérie Berthé ◽  
Charles Holton ◽  
Luca Q. Zamboni
Keyword(s):  
Sturmian Sequences

scholarly journals Language complexity of rotations and Sturmian sequences

1998 ◽  
Vol 209 (1-2) ◽  
pp. 179-193 ◽  
Author(s):  
François Blanchard ◽  
Petr Kůrka
Keyword(s):  
Language Complexity ◽  
Sturmian Sequences

scholarly journals A Characterization of Balanced Episturmian Sequences

10.37236/951 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Geneviève Paquin ◽  
Laurent Vuillon
Keyword(s):  
Natural Generalization ◽  
Periodic Sequences ◽  
Letter Alphabet ◽  
Sturmian Sequences ◽  
Special Case

It is well-known that Sturmian sequences are the non ultimately periodic sequences that are balanced over a 2-letter alphabet. They are also characterized by their complexity: they have exactly $(n+1)$ distinct factors of length $n$. A natural generalization of Sturmian sequences is the set of infinite episturmian sequences. These sequences are not necessarily balanced over a $k$-letter alphabet, nor are they necessarily aperiodic. In this paper, we characterize balanced episturmian sequences, periodic or not, and prove Fraenkel's conjecture for the special case of episturmian sequences. It appears that balanced episturmian sequences are all ultimately periodic and they can be classified in 3 families.

Study on Properties of Expanded Sturmian Sequences

2013 ◽  
Vol 756-759 ◽  
pp. 1536-1540
Author(s):  
Li Hua Sun ◽  
En Liang Zhao ◽  
Yan Ling Sun
Keyword(s):  
Symbolic Dynamics ◽  
Special Kind ◽  
Practical Applications ◽  
Symbolic Space ◽  
Iterative System ◽  
Sturmian Sequences

Symbolic dynamics is an iterative system that is generated by a shift on a finite symbolic space. It is a special kind of dynamics. Symbolic dynamics has a lot of theoretical and practical applications in many fields such as physics, computer and so on, so it is important to study its dynamical behavior.Sturmian system that is generated by Sturmian sequences is the least complex kind of symbolic dynamics. In the present paper Sturmian sequences are expanded which make them generality. In fact expanded Sturmian sequences share many of properties of Sturmian sequences, but they cannot completely take place of Sturmian sequences. It appears to make a difference between them. It is of value to study expanded Sturmian sequences.

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