Palindromes in Sturmian Words

  • Aldo de Luca
  • Alessandro De Luca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


We study some structural and combinatorial properties of Sturmian palindromes, i.e., palindromic finite factors of Sturmian words. In particular, we give a formula which permits to compute in an exact way the number of Sturmian palindromes of any length. Moreover, an interesting characterization of Sturmian palindromes is obtained.


Special Factor Minimal Period Combinatorial Property Median Factor Empty Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allouche, J.P., Shallit, J.: Automatic Sequences, ch. 9-10. Cambridge University Press, Cambridge (2003)zbMATHCrossRefGoogle Scholar
  2. 2.
    Berstel, J., Séébold, P.: Sturmian words. In: Lothaire, M. (ed.) Algebraic Combinatorics on Words, ch. 2. Cambridge University Press, Cambridge (2001)Google Scholar
  3. 3.
    Borel, J.P., Reutenauer, C.: Palindromic factors of billiard words. Theoretical Computer Science (2005) (to appear)Google Scholar
  4. 4.
    Carpi, A.: Private communication (2005)Google Scholar
  5. 5.
    D’Alessandro, F.: A combinatorial problem on Trapezoidal words. Theoretical Computer Science 273, 11–33 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    de Luca, A.: On the combinatorics of finite words. Theoretical Computer Science 218, 13–39 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    de Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theoretical Computer Science 183, 45–82 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    de Luca, A., Mignosi, F.: Some combinatorial properties of Sturmian words. Theoretical Computer Science 136, 361–385 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Droubay, X., Pirillo, G.: Palindromes and Sturmian words. Theoretical Computer Science 223, 73–85 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading (1983)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Aldo de Luca
    • 1
  • Alessandro De Luca
    • 1
  1. 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università degli Studi di Napoli Federico IINapoliItaly

Personalised recommendations