Displaying similar documents to “A note on univoque self-Sturmian numbers”

On the product of balanced sequences

Antonio Restivo, Giovanna Rosone (2012)

RAIRO - Theoretical Informatics and Applications

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The product  =  ⊗  of two sequences and is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product of two balanced sequences is balanced too. In the case and are binary sequences, we prove, as a main result, that, if such a product is balanced and () = 4, then is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems proposed...

On the product of balanced sequences

Antonio Restivo, Giovanna Rosone (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

The product  =  ⊗  of two sequences and is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product of two balanced sequences is balanced too. In the case and are binary sequences, we prove, as a main result, that, if such a product is balanced and () = 4, then is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems proposed...

On synchronized sequences and their separators

Arturo Carpi, Cristiano Maggi (2010)

RAIRO - Theoretical Informatics and Applications

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We introduce the notion of a -synchronized sequence, where is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be -synchronized if its graph is represented, in base , by a right synchronized rational relation. This is an intermediate notion between -automatic and -regular sequences. Indeed, we show that the class of -automatic sequences is equal to the class of bounded -synchronized sequences and that the class of -synchronized sequences...

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When =1 we show that . In the cases when or max} we show that the first difference of the complexity function takes value in for every , and consequently we determine...

A note on constructing infinite binary words with polynomial subword complexity

Francine Blanchet-Sadri, Bob Chen, Sinziana Munteanu (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Most of the constructions of infinite words having polynomial subword complexity are quite complicated, , sequences of Toeplitz, sequences defined by billiards in the cube, etc. In this paper, we describe a simple method for constructing infinite words over a binary alphabet  {  }  with polynomial subword complexity . Assuming contains an infinite number of ’s, our method is based on the gap function which gives the distances between consecutive ’s. It is known that...

On the distribution of characteristic parameters of words

Arturo Carpi, Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

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For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...