Morphisms fixing words associated with exchange of three intervals

Petr Ambrož; Zuzana Masáková; Edita Pelantová

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 1, page 3-17
  • ISSN: 0988-3754

Abstract

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We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.

How to cite

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Ambrož, Petr, Masáková, Zuzana, and Pelantová, Edita. "Morphisms fixing words associated with exchange of three intervals." RAIRO - Theoretical Informatics and Applications 44.1 (2010): 3-17. <http://eudml.org/doc/250796>.

@article{Ambrož2010,
abstract = { We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability. },
author = {Ambrož, Petr, Masáková, Zuzana, Pelantová, Edita},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Interval exchange transformation; Sturmian morphisms; substitution invariance.; interval exchange transformation; substitution invariance},
language = {eng},
month = {2},
number = {1},
pages = {3-17},
publisher = {EDP Sciences},
title = {Morphisms fixing words associated with exchange of three intervals},
url = {http://eudml.org/doc/250796},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Ambrož, Petr
AU - Masáková, Zuzana
AU - Pelantová, Edita
TI - Morphisms fixing words associated with exchange of three intervals
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/2//
PB - EDP Sciences
VL - 44
IS - 1
SP - 3
EP - 17
AB - We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.
LA - eng
KW - Interval exchange transformation; Sturmian morphisms; substitution invariance.; interval exchange transformation; substitution invariance
UR - http://eudml.org/doc/250796
ER -

References

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  1. B. Adamczewski, Codages de rotations et phénomènes d'autosimilarité. J. Théor. Nombres Bordeaux14 (2002) 351–386.  
  2. C. Allauzen, Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux10 (1998) 237–241.  
  3. P. Arnoux, V. Berthé, Z. Masáková and E. Pelantová, Sturm numbers and substitution invariance of 3iet words. Integers8 (2008) 17 (electronic).  
  4. P. Baláži, Z. Masáková and E. Pelantová, Complete characterization of substitution invariant Sturmian sequences. Integers5 (2005) 23 (electronic).  
  5. P. Baláži, Z. Masáková and E. Pelantová, Characterization of substitution invariant 3iet words. Integers8 (2008) 21 (electronic).  
  6. J. Berstel and P. Séébold, Morphismes de Sturm. Bull. Belg. Math. Soc. Simon Stevin1 (1994) 175–189. Journées Montoises (Mons, 1992).  
  7. V. Berthé, H. Ei, S. Ito and H. Rao, On substitution invariant Sturmian words: an application of Rauzy fractals. RAIRO-Theor. Inf. Appl.41 (2007) 329–349.  
  8. M.D. Boshernitzan and C.R. Carroll, An extension of Lagrange's theorem to interval exchange transformations over quadratic fields. J. Anal. Math.72 (1997) 21–44.  
  9. D. Crisp, W. Moran, A. Pollington and P. Shiue, Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux5 (1993) 123–137.  
  10. S. Ferenczi, C. Holton and L.Q. Zamboni, Structure of three interval exchange transformations. I. An arithmetic study. Ann. Inst. Fourier51 (2001) 861–901.  
  11. S. Ferenczi, C. Holton and L.Q. Zamboni, Structure of three-interval exchange transformations. II. A combinatorial description of the trajectories. J. Anal. Math.89 (2003) 239–276.  
  12. S. Ferenczi, C. Holton and L.Q. Zamboni, Structure of three-interval exchange transformations III: ergodic and spectral properties. J. Anal. Math.93 (2004) 103–138.  
  13. M. Fiedler, Special matrices and their applications in numerical mathematics. Martinus Nijhoff Publishers, Dordrecht (1986). Translated from the Czech by Petr Přikryl and Karel Segeth.  
  14. T. Komatsu and A.J. van der Poorten, Substitution invariant Beatty sequences. Jpn J. Math. (N.S.)22 (1996) 349–354.  
  15. F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux5 (1993) 221–233.  
  16. B. Parvaix, Substitution invariant Sturmian bisequences. J. Théor. Nombres Bordeaux11 (1999) 201–210. Les XXèmes Journées Arithmétiques (Limoges, 1997).  
  17. M. Queffélec, Substitution dynamical systems–spectral analysis. Lect. Notes Math. 1294 (1987).  
  18. P. Séébold, Fibonacci morphisms and Sturmian words. Theoret. Comput. Sci.88 (1991) 365–384.  
  19. S.-I. Yasutomi, On Sturmian sequences which are invariant under some substitutions. In Number theory and its applications (Kyoto, 1997), Dev. Math.2, Kluwer Acad. Publ. (1999) 347–373.  

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