Wolfgang Steiner (2012)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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The (−)-integers are natural generalisations of the -integers, and thus of the integers, for negative real bases. When is the analogue of a Parry number, we describe the structure of the set of (−)-integers by a fixed point of an anti-morphism.
Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)
RAIRO - Theoretical Informatics and Applications
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We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny (2004) use it.
Z. Masáková, T. Vávra (2014)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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We consider numeration systems with base and − , for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets Z and Z of numbers with integer expansion in base , resp. − . Our main result is the comparison of languages of infinite words and coding the ordering of distances between consecutive - and (− )-integers. It turns out that for a class of roots of − − , the languages coincide, while for other...
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...
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 ...
Antonio Restivo, Giovanna Rosone (2012)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et 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...
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...
József Balogh, Béla Bollobás (2010)
RAIRO - Theoretical Informatics and Applications
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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...
Antonio Restivo, Giovanna Rosone (2012)
RAIRO - Theoretical Informatics and 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...