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On Christoffel classes

Published online by Cambridge University Press:  15 October 2005

Jean-Pierre Borel  and
Christophe Reutenauer
Jean-Pierre Borel
Affiliation:
LACO, UMR CNRS 6090, 123 avenue Albert Thomas, 87060 Limoges Cedex, France; borel@unilim.fr
Christophe Reutenauer
Affiliation:
Université du Québec à Montréal; Département de mathématiques; Case postale 8888, succursale Centre-Ville, Montréal (Québec) H3C 3P8, Canada; christo@math.uqam.ca
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Abstract

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.

Keywords

WordsChristoffelsturmianconjugationgeometric.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 1 , January 2006 , pp. 15 - 27
Copyright
© EDP Sciences, 2006

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References

J.-P. Allouche and J. Shallit, Automatic sequences. Cambridge (2003).
J. Berstel, Tracé de droites, fractions continues et morphismes itérés, in M. Lothaire, Mots, mélanges offerts M.-P. Schtzenberger, Hermès, Paris (1990) 298–309.
J. Berstel and P. Séébold, Sturmian words, in M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press (2002) 45–110.
Borel, J.-P. and Laubie, F., Quelques mots sur la droite projective réelle. J. Théorie des Nombres de Bordeaux 5 (1993) 23–51. CrossRef
Berstel, J. and de Luca, A., Sturmian words, Lyndon words and trees. Theor. Comput. Sci. 178 (1997) 171–2003. CrossRef
Christoffel, E.B., Observatio arithmetica. Annali di Matematica 6 (1875) 148–152. CrossRef
Chuan, W.-F., α-words and factors of characteristic sequences. Discrete Math. 177 (1997) 33–50. CrossRef
Chuan, W.-F., Characterizations of α-words, moments, and determinants. Fibonacci Quart. 41 (2003) 194–208.
Chuan, W.-F., Moments of conjugacy classes of binary words. Theor. Comput. Sci. 310 (2004) 273–285. CrossRef
W.-F. Chuan, Factors of characteristic words of irrational numbers. Preprint.
Cohn, H., Markoff forms and primitive words. Math. Ann. 196 (1972) 8–22. CrossRef
de Luca, A., Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183 (1997) 45–82. CrossRef
A. de Luca and F. Mignosi, On some combinatorial properties of Sturmian words. Theor. Compt. Sci. 136 (1994) 361–385.
Mantaci, S., Restivo, A. and Sciortino, M., Burrows-Wheeler transform and Sturmian words. Inform. Proc. Lett. 86 (2003) 241–246. CrossRef
Pirillo, G., A new characteristic property of the palindrome prefixes of a standard sturmian word. Sém. Lothar. Combin. 43 (1999) 1–3.
G. Pirillo, A curious characteristic property of standard Sturmian word, in Algebraic Combinatorics, Computer Science, edited by H. Crapo and D. Senato. Springer (2001) 541–546.