A little more about morphic Sturmian words

Isabelle Fagnot

RAIRO - Theoretical Informatics and Applications (2006)

  • Volume: 40, Issue: 3, page 511-518
  • ISSN: 0988-3754

Abstract

top
Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial proof of this result.

How to cite

top

Fagnot, Isabelle. "A little more about morphic Sturmian words." RAIRO - Theoretical Informatics and Applications 40.3 (2006): 511-518. <http://eudml.org/doc/249722>.

@article{Fagnot2006,
abstract = { Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial proof of this result. },
author = {Fagnot, Isabelle},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Sturmian words; infinite words; iterated morphisms; combinatorics of words.; combinatorics of words},
language = {eng},
month = {10},
number = {3},
pages = {511-518},
publisher = {EDP Sciences},
title = {A little more about morphic Sturmian words},
url = {http://eudml.org/doc/249722},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Fagnot, Isabelle
TI - A little more about morphic Sturmian words
JO - RAIRO - Theoretical Informatics and Applications
DA - 2006/10//
PB - EDP Sciences
VL - 40
IS - 3
SP - 511
EP - 518
AB - Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and Sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial proof of this result.
LA - eng
KW - Sturmian words; infinite words; iterated morphisms; combinatorics of words.; combinatorics of words
UR - http://eudml.org/doc/249722
ER -

References

top
  1. C. Allauzen, Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux10 (1998) 237–241.  Zbl0930.11051
  2. J. Berstel and P. Séébold, A remark on morphic sturmian words. Theor. Inform. Appl.28 (1994) 255–263.  Zbl0883.68104
  3. J. Berstel and P. Séébold, Algebraic combinatorics on Words, chapter Sturmian words. Cambridge University Press (2002).  Zbl0883.68104
  4. V. Berthé, H. Ei, S. Ito and H. Rao, Invertible susbtitutions and Sturmian words: an application of Rauzy fractals. Preprint.  Zbl1140.11014
  5. D. Crisp, W. Moran, A. Pollington and P. Shiue, Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux5 (1993) 123–137.  Zbl0786.11041
  6. J. Justin and G. Pirillo, Episturmian words: Shifts, morphisms and numeration systems. Inter. J. Found. Comput. Sci.15 (2004) 329–348.  Zbl1067.68115
  7. F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux5 (1993) 221–233.  
  8. B. Parvaix, Propriétés d'invariance des mots sturmiens. J. Théor. Nombres Bordeaux9 (1997) 351–369.  
  9. Shin-Ichi Yasutomi, On sturmian sequences which are invariant under some substitutions, in Number theory and its applications. Proceedings of the conference held at the RIMS, Kyoto, Japan, November 10–14, 1997, edited by Kanemitsu, Shigeru et al. Kluwer Acad. Publ. Dordrecht (1999) 347–373.  Zbl0971.11007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.