Initial powers of Sturmian sequences

Berthé, Valérie; Holton, Charles; Zamboni, Luca Q.

doi:10.4064/aa122-4-1

Cited by 61 publications

(83 citation statements)

References 45 publications

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“…III.7] on S-adic representations for standard Arnoux-Rauzy sequences. See also the recent paper [23] for S-adic representations of Sturmian words. Note that S-adic dynamical systems were introduced by Ferenczi [50] as minimal dynamical systems (e.g., see [96]) generated by a finite number of substitutions.…”

Section: Relation With Episturmian Wordsmentioning

confidence: 99%

Episturmian words: a survey

Glen

Justin

2009

RAIRO-Theor. Inf. Appl.

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In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties of episturmian words, as well as their connection to the balance property, and related notions such as finite episturmian words, Arnoux-Rauzy sequences, and "episkew words" that generalize the skew words of Morse and Hedlund.

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Section: Relation With Episturmian Wordsmentioning

confidence: 99%

Episturmian words: a survey

Glen

Justin

2009

RAIRO-Theor. Inf. Appl.

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“…III.7] on S-adic representations for characteristic Arnoux-Rauzy sequences. See also the recent paper [4] for S-adic representations of Sturmian words. Note that S-adic dynamical systems were introduced by Ferenczi [6] as minimal dynamical systems (e.g., see [23]) generated by a finite number of substitutions.…”

Section: Remark 23 [13]mentioning

confidence: 99%

“…In Section 5 we have proposed a way to uniquely define any episturmian word through a normalization of its directives words (as mentioned in the introduction; see [4,11,17,18] for some of its uses). Using these results we now characterize episturmian words having a unique directive word.…”

Section: Now We Provide Thementioning

confidence: 99%

Directive words of episturmian words: equivalences and normalization

Glen

Levé

Richomme

2008

RAIRO-Theor. Inf. Appl.

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Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.

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“…. The initial critical exponent of a, introduced by Berthé, Holton and Zamboni [11] and denoted by ice(a), is the supremum of the real numbers x for which there exist arbitrarily long prefixes of a that can be expressed in the form V x , for a finite word V .…”

Section: The Initial Critical Exponent and The Diophantine Exponentmentioning

confidence: 99%

Quadratic approximation to automatic continued fractions

Bugeaud¹

2015

J. Théor. Nombres Bordeaux

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Initial powers of Sturmian sequences

Cited by 61 publications

References 45 publications

Episturmian words: a survey

Episturmian words: a survey

Directive words of episturmian words: equivalences and normalization

Quadratic approximation to automatic continued fractions

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