Displaying similar documents to “Complete characterization of substitution invariant Sturmian sequences.”

Morphisms fixing words associated with exchange of three intervals

Petr Ambrož, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.

On substitution invariant Sturmian words: an application of Rauzy fractals

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

RAIRO - Theoretical Informatics and Applications

Similarity:

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 ...

Substitution invariant sturmian bisequences

Bruno Parvaix (1999)

Journal de théorie des nombres de Bordeaux

Similarity:

We prove that a Sturmian bisequence, with slope α and intercept ρ , is fixed by some non-trivial substitution if and only if α is a Sturm number and ρ belongs to ℚ ( α ) . We also detail a complementary system of integers connected with Beatty bisequences.

How to build billiard words using decimations

Jean-Pierre Borel (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

We present two methods based on decimation for computing finite billiard words on any finite alphabet. The first method computes finite billiard words by iteration of some transformation on words. The number of iterations is explicitly bounded. The second one gives a direct formula for the billiard words. Some results remain true for infinite standard Sturmian words, but cannot be used for computation as they only are limit results.

Standard factors of Sturmian words

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

RAIRO - Theoretical Informatics and Applications

Similarity:

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.