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Study of Christoffel Classes: Normal Form and Periodicity

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Combinatorics on Words (WORDS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10432))

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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).

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References

  1. Berstel, J.: Tracé de droites, fractions continues et morphismes itérés. Mots, pp. 298–309 (1990)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. Berstel, J., de Luca, A.: Sturmian words, Lyndon words and trees. Theoret. Comput. Sci. 178(1–2), 171–203 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Borel, J.P., Laubie, F.: Quelques mots sur la droite projective réelle. J. Théor. Nombres Bordeaux 5, 15–27 (1993)

    MATH  Google Scholar 

  5. Borel, J.P., Reutenauer, C.: On Christoffel classes. RAIRO Theor. Inf. Appl. 40(1), 15–27 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chuan, W.F.: \(\alpha \)-words and factors of characteristic sequences. Discrete Math. 177, 33–50 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Currie, J.D., Saari, K.: Least periods of factors of infinite words. Theor. Inform. Appl. 43(1), 165–178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hegedüs, L., Nagy, B.: On periodic properties of circular words. Discrete Math. 339(3), 1189–1197 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lothaire, M.: Combinatorics on Words. Addison Wesley, Boston (1983)

    MATH  Google Scholar 

  10. de Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183, 45–82 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. de Luca, A., Luca, A.D.: Some caracterizations of finite Sturmian words. Theor. Comput. Sci. 356, 557–5573 (2006)

    Google Scholar 

  12. de Luca, A., Mignosi, F.: Some combinatorial properties of Sturmian palindromes. Theor. Comput. Sci. 136(2), 541–546 (1994)

    Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. Reutenauer, C.: Studies on finite Sturmian words. Theor. Comput. Sci. 591, 106–133 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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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).

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Authors and Affiliations

  1. Laboratoire de Combinatoire et d’Informatique Mathématique, Université du Québec à Montréal, Montréal, Canada

    Mélodie Lapointe

Authors
  1. Mélodie Lapointe
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Correspondence to Mélodie Lapointe .

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Editors and Affiliations

  1. Université du Québec à Montréal, Montreal, Québec, Canada

    Srečko Brlek

  2. Université du Québec à Montréal, Montreal, Québec, Canada

    Francesco Dolce

  3. Université du Québec à Montréal, Montreal, Québec, Canada

    Christophe Reutenauer

  4. Université du Québec à Montréal, Montreal, Québec, Canada

    Élise Vandomme

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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

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  • DOI: https://doi.org/10.1007/978-3-319-66396-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66395-1

  • Online ISBN: 978-3-319-66396-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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