Abstract
We characterize the left normal forms of conjugates of Christoffel words and compute their minimal period. This answers two open questions in Reutenauer (2015).
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Berstel, J.: Tracé de droites, fractions continues et morphismes itérés. Mots, pp. 298–309 (1990)
Berstel, J., Lauve, A., Reutenauer, C., Saliola, F.: Combinatorics on words: Christoffel words and repetitions in words. CRM Monograph Series, 27. American Mathematical Society, Providence (2009)
Berstel, J., de Luca, A.: Sturmian words, Lyndon words and trees. Theoret. Comput. Sci. 178(1–2), 171–203 (1997)
Borel, J.P., Laubie, F.: Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5, 15–27 (1993)
Borel, J.P., Reutenauer, C.: On Christoffel classes. RAIRO Theor. Inf. Appl. 40(1), 15–27 (2006)
Chuan, W.F.: \(\alpha \)-words and factors of characteristic sequences. Discrete Math. 177, 33–50 (1997)
Currie, J.D., Saari, K.: Least periods of factors of infinite words. Theor. Inform. Appl. 43(1), 165–178 (2009)
Hegedüs, L., Nagy, B.: On periodic properties of circular words. Discrete Math. 339(3), 1189–1197 (2016)
Lothaire, M.: Combinatorics on Words. Addison Wesley, Boston (1983)
de Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183, 45–82 (1997)
de Luca, A., Luca, A.D.: Some caracterizations of finite Sturmian words. Theor. Comput. Sci. 356, 557–5573 (2006)
de Luca, A., Mignosi, F.: Some combinatorial properties of Sturmian palindromes. Theor. Comput. Sci. 136(2), 541–546 (1994)
Pirillo, G.: A curious characteristic property of standard Sturmian words. In: Crapo, H., Senato, D. (eds.) Algebraic Combinatorics and Computer Science, pp. 541–546. Springer, Milano (2001)
Reutenauer, C.: Studies on finite Sturmian words. Theor. Comput. Sci. 591, 106–133 (2015)
Acknowledgments
I would like to thank Christophe Reutenauer, Srecko Brlek, Alexandre Blondin Massé and Sébastien Labbé for their suggestions and their helpful comments. I was supported by NSERC (Canada).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Lapointe, M. (2017). Study of Christoffel Classes: Normal Form and Periodicity. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-66396-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66395-1
Online ISBN: 978-3-319-66396-8
eBook Packages: Computer ScienceComputer Science (R0)