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How to build billiard words using decimations

Jean-Pierre Borel — 2010

RAIRO - Theoretical Informatics and Applications

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.

On Christoffel classes

Jean-Pierre BorelChristophe Reutenauer — 2006

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

On Christoffel classes

Jean-Pierre BorelChristophe Reutenauer — 2010

RAIRO - Theoretical Informatics and Applications

We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

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