Abstract
A word w is central if it has two periods p and q which are coprime and such that |w|= p+q–2. Central words play an essential role in the combinatorics of Sturmian words. The aim of this paper is to give an overview on central words focusing some recent developments in the study of their structure, combinatorics, and arithmetics. Moreover, some results are concerned with remarkable languages of central words such as central codes and Farey’s codes. Another interesting class of central languages is given by the so-called Farey languages which give faithful representations of Farey’s series.
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Allouche, J.-P., Shallit, J.: Automatic Sequences. Cambridge University Press, Cambridge (2003)
Berstel, J., de Luca, A.: Sturmian words, Lyndon words and trees. Theoretical Computer Science 178, 171–203 (1997)
Berstel, J., Perrin, D.: Theory of Codes. Academic Press, New York (1985)
Berstel, J., Séébold, P.: Sturmian words. In: Lothaire, M. (ed.) Algebraic Combinatorics on Words, pp. 45–110. Cambridge University Press, Cambridge (2002)
Borel, J.P., Reutenauer, C.: Palindromic factors of billiard words. Theoretical Computer Science (to appear)
Burrows, M., Wheeler, D.J.: A block sorting data compression algorithm. Technical report, DIGITAL System Research Center (1994)
Carpi, A., de Luca, A.: Harmonic and gold Sturmian words. European Journal of Combinatorics 25, 685–705 (2004)
Carpi, A., de Luca, A.: Codes of central Sturmian words. Theoretical Computer Science (to appear)
Carpi, A., de Luca, A.: Farey codes and languages (Manuscript, 2005)
de Luca, A.: Combinatorics of standard Sturmian words. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 249–267. Springer, Heidelberg (1997)
de Luca, A.: Standard Sturmian morphisms. Theoretical Computer Science 178, 205–224 (1997)
de Luca, A.: Sturmian words: structure, combinatorics, and their arithmetics. Theoretical Computer Science 183, 45–82 (1997)
de Luca, A., De Luca, A.: Palindromes in Sturmian words. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 199–208. Springer, Heidelberg (2005)
de Luca, A., Mignosi, F.: On some combinatorial properties of Sturmian words. Theoretical Computer Science 136, 361–385 (1994)
Edwards, H.M.: Riemann’s Zeta Function. Academic Press, New York (1974)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Oxford University Press, Oxford (1968)
Ilie, L., Plandowski, W.: Two-variable word equations. Theoretical Informatics and Applications 34, 467–501 (2000)
Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading (1983); 2nd edn. Cambridge University Press Cambridge (1997)
Mantaci, S., Restivo, A., Sciortino, M.: Burrows-Wheeler transform and Sturmian words. Information Processing Letters 86, 241–246 (2003)
Mignosi, F.: On the number of factors of Sturmian words. Theoretical Computer Science 82, 71–84 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carpi, A., de Luca, A. (2005). Central Sturmian Words: Recent Developments. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_4
Download citation
DOI: https://doi.org/10.1007/11505877_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26546-7
Online ISBN: 978-3-540-31682-4
eBook Packages: Computer ScienceComputer Science (R0)