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.
Mots clés : words, Christoffel, sturmian, conjugation, geometric
@article{ITA_2006__40_1_15_0, author = {Borel, Jean-Pierre and Reutenauer, Christophe}, title = {On {Christoffel} classes}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {15--27}, publisher = {EDP-Sciences}, volume = {40}, number = {1}, year = {2006}, doi = {10.1051/ita:2005038}, mrnumber = {2197281}, zbl = {1085.68116}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2005038/} }
TY - JOUR AU - Borel, Jean-Pierre AU - Reutenauer, Christophe TI - On Christoffel classes JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 15 EP - 27 VL - 40 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2005038/ DO - 10.1051/ita:2005038 LA - en ID - ITA_2006__40_1_15_0 ER -
%0 Journal Article %A Borel, Jean-Pierre %A Reutenauer, Christophe %T On Christoffel classes %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 15-27 %V 40 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2005038/ %R 10.1051/ita:2005038 %G en %F ITA_2006__40_1_15_0
Borel, Jean-Pierre; Reutenauer, Christophe. On Christoffel classes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 1, pp. 15-27. doi : 10.1051/ita:2005038. http://www.numdam.org/articles/10.1051/ita:2005038/
[1] Automatic sequences. Cambridge (2003). | MR | Zbl
and ,[2] Tracé de droites, fractions continues et morphismes itérés, in M. Lothaire, Mots, mélanges offerts M.-P. Schtzenberger, Hermès, Paris (1990) 298-309.
,[3] Sturmian words, in M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press (2002) 45-110.
and ,[4] Quelques mots sur la droite projective réelle. J. Théorie des Nombres de Bordeaux 5 (1993) 23-51. | Numdam | Zbl
and ,[5] Sturmian words, Lyndon words and trees. Theor. Comput. Sci. 178 (1997) 171-2003. | Zbl
and ,[6] Observatio arithmetica. Annali di Matematica 6 (1875) 148-152. | JFM
,[7] -words and factors of characteristic sequences. Discrete Math. 177 (1997) 33-50. | Zbl
,[8] Characterizations of -words, moments, and determinants. Fibonacci Quart. 41 (2003) 194-208. | Zbl
,[9] Moments of conjugacy classes of binary words. Theor. Comput. Sci. 310 (2004) 273-285. | Zbl
,[10] Factors of characteristic words of irrational numbers. Preprint. | MR | Zbl
,[11] Markoff forms and primitive words. Math. Ann. 196 (1972) 8-22. | Zbl
,[12] Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183 (1997) 45-82. | Zbl
,[13] On some combinatorial properties of Sturmian words. Theor. Compt. Sci. 136 (1994) 361-385. | Zbl
and ,[14] Burrows-Wheeler transform and Sturmian words. Inform. Proc. Lett. 86 (2003) 241-246.
, and ,[15] A new characteristic property of the palindrome prefixes of a standard sturmian word. Sém. Lothar. Combin. 43 (1999) 1-3. | Zbl
,[16] A curious characteristic property of standard Sturmian word, in Algebraic Combinatorics, Computer Science, edited by H. Crapo and D. Senato. Springer (2001) 541-546. | Zbl
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