Displaying similar documents to “Connectedness of fractals associated with Arnoux–Rauzy substitutions”

Study of irreducible balanced pairs for substitutive languages

Julien Bernat (2008)

RAIRO - Theoretical Informatics and Applications

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Let ℒ be a language. A balanced pair consists of two words and in ℒ which have the same number of occurrences of each letter. It is irreducible if the pairs of strict prefixes of and of the same length do not form balanced pairs. In this article, we are interested in computing the set of irreducible balanced pairs on several cases of languages. We make connections with the balanced pairs algorithm and discrete geometrical constructions related to substitutive languages. We characterize...

On substitution invariant Sturmian words: an application of Rauzy fractals

Valérie Berthé, Hiromi Ei, Shunji Ito, Hui Rao (2007)

RAIRO - Theoretical Informatics and Applications

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Sturmian words are infinite words that have exactly factors of length for every positive integer . A Sturmian word is also defined as a coding over a two-letter alphabet of the orbit of point under the action of the irrational rotation (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investigate Rauzy fractals associated with two-letter invertible substitutions. As an application, we give an alternative ...

On a characteristic property of ARNOUX–RAUZY sequences

Jacques Justin, Giuseppe Pirillo (2010)

RAIRO - Theoretical Informatics and Applications

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Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.

Standard factors of Sturmian words

Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)

RAIRO - Theoretical Informatics and Applications

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Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word , some standard words occur that are not prefixes of . We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.