Existence of an infinite ternary 64-abelian square-free word

Mari Huova

Displaying similar documents to “Existence of an infinite ternary 64-abelian square-free word”

Abelian pattern avoidance in partial words

F. Blanchet-Sadri, Benjamin De Winkle, Sean Simmons (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Pattern avoidance is an important topic in combinatorics on words which dates back to the beginning of the twentieth century when Thue constructed an infinite word over a ternary alphabet that avoids squares, , a word with no two adjacent identical factors. This result finds applications in various algebraic contexts where more general patterns than squares are considered. On the other hand, Erdős raised the question as to whether there exists an infinite word that avoids abelian squares,...

5-abelian cubes are avoidable on binary alphabets

Robert Mercaş, Aleksi Saarela (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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A -abelian cube is a word , where the factors , , and are either pairwise equal, or have the same multiplicities for every one of their factors of length at most . Previously it has been shown that -abelian cubes are avoidable over a binary alphabet for ≥ 8. Here it is proved that this holds for ≥ 5.

Finite repetition threshold for large alphabets

Golnaz Badkobeh, Maxime Crochemore, Michaël Rao (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We investigate the finite repetition threshold for -letter alphabets, ≥ 4, that is the smallest number for which there exists an infinite -free word containing a finite number of -powers. We show that there exists an infinite Dejean word on a 4-letter alphabet (a word without factors of exponent more than 7/5 ) containing only two 7/5 -powers. For a 5-letter alphabet, we show that there exists an infinite Dejean word containing only 60 5/4 -powers, and we conjecture...

An aperiodicity problem for multiwords

Véronique Bruyère, Olivier Carton, Alexandre Decan, Olivier Gauwin, Jef Wijsen (2012)

RAIRO - Theoretical Informatics and Applications

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Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word is in a multiword if it occurs in word that can be obtained by selecting one single symbol among the symbols provided in each position of . Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word is certain in a multiword . We study the language CERTAIN() of multiwords...

An aperiodicity problem for multiwords

Véronique Bruyère, Olivier Carton, Alexandre Decan, Olivier Gauwin, Jef Wijsen (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Look and Say Fibonacci

Patrice Séébold (2010)

RAIRO - Theoretical Informatics and Applications

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The () derivative of a word is obtained by writing the number of consecutive equal letters when the word is spelled from left to right. For example, 1 1 2 3 3) = 2 1 1 2 2 3 (two , one , two ). We start the study of the behaviour of binary words generated by morphisms under the operator, focusing in particular on the Fibonacci word.

Forbidden Factors and Fragment Assembly

F. Mignosi, A. Restivo, M. Sciortino (2010)

RAIRO - Theoretical Informatics and Applications

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In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word from a given set of substrings () of a word . We introduce an hypothesis involving the set of fragments and the maximal length of the minimal forbidden factors of . Such hypothesis allows us to reconstruct uniquely the word from the set in linear time....

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...