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On a Generalization of Standard Episturmian Morphisms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5257))

Abstract

In a recent paper with L. Q. Zamboni the authors introduced the class of ϑ-episturmian words, where ϑ is an involutory antimorphism of the free monoid A *. In this paper, we introduce and study ϑ-characteristic morphisms, that is, morphisms which map standard episturmian words into standard ϑ-episturmian words. They are a natural extension of standard episturmian morphisms. The main result of the paper is a characterization of these morphisms when they are injective.

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References

  1. Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  2. Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  3. Lothaire, M.: Applied Combinatorics on Words. Cambridge University Press, Cambridge (2005)

    MATH  Google Scholar 

  4. Droubay, X., Justin, J., Pirillo, G.: Episturmian words and some constructions of de Luca and Rauzy. Theoretical Computer Science 255, 539–553 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Justin, J., Pirillo, G.: Episturmian words and episturmian morphisms. Theoretical Computer Science 276, 281–313 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fischler, S.: Palindromic prefixes and episturmian words. Journal of Combinatorial Theory, Series A 113, 1281–1304 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. de Luca, A., De Luca, A.: Pseudopalindrome closure operators in free monoids. Theoretical Computer Science 362, 282–300 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bucci, M., de Luca, A., De Luca, A., Zamboni, L.Q.: On some problems related to palindrome closure. Theoretical Informatics and Applications (to appear, 2008), doi:10.1051/ita:2007064

    Google Scholar 

  9. Bucci, M., de Luca, A., De Luca, A., Zamboni, L.Q.: On different generalizations of episturmian words. Theoretical Computer Science 393, 23–36 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bucci, M., de Luca, A., De Luca, A., Zamboni, L.Q.: On θ-episturmian words. European Journal of Combinatorics (to appear, 2008)

    Google Scholar 

  11. Bucci, M., de Luca, A., De Luca, A.: Characteristic morphisms of generalized episturmian words. Preprint n. 18, DMA “R. Caccioppoli” (2008)

    Google Scholar 

  12. Berstel, J., Perrin, D.: Theory of Codes. Academic Press, New York (1985)

    MATH  Google Scholar 

  13. de Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theoretical Computer Science 183, 45–82 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  14. Justin, J.: Episturmian morphisms and a Galois theorem on continued fractions. Theoretical Informatics and Applications 39, 207–215 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Masami Ito Masafumi Toyama

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© 2008 Springer-Verlag Berlin Heidelberg

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Bucci, M., de Luca, A., De Luca, A. (2008). On a Generalization of Standard Episturmian Morphisms. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-85780-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85779-2

  • Online ISBN: 978-3-540-85780-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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