Morphisms fixing words associated with exchange of three intervals
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 3-17.

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.

DOI : 10.1051/ita/2010002
Classification : 68R15, 08A50
Mots-clés : interval exchange transformation, sturmian morphisms, substitution invariance 
@article{ITA_2010__44_1_3_0,
     author = {Ambro\v{z}, Petr and Mas\'akov\'a, Zuzana and Pelantov\'a, Edita},
     title = {Morphisms fixing words associated with exchange of three intervals},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {3--17},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ita/2010002},
     mrnumber = {2604932},
     zbl = {1186.68342},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita/2010002/}
}
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 - Informatique Théorique et Applications
PY  - 2010
SP  - 3
EP  - 17
VL  - 44
IS  - 1
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita/2010002/
DO  - 10.1051/ita/2010002
LA  - en
ID  - ITA_2010__44_1_3_0
ER  - 
%0 Journal Article
%A Ambrož, Petr
%A Masáková, Zuzana
%A Pelantová, Edita
%T Morphisms fixing words associated with exchange of three intervals
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2010
%P 3-17
%V 44
%N 1
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita/2010002/
%R 10.1051/ita/2010002
%G en
%F ITA_2010__44_1_3_0
Ambrož, Petr; Masáková, Zuzana; Pelantová, Edita. Morphisms fixing words associated with exchange of three intervals. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 3-17. doi : 10.1051/ita/2010002. http://archive.numdam.org/articles/10.1051/ita/2010002/

[1] B. Adamczewski, Codages de rotations et phénomènes d'autosimilarité. J. Théor. Nombres Bordeaux 14 (2002) 351-386. | Zbl

[2] C. Allauzen, Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux 10 (1998) 237-241. | Numdam | Zbl

[3] P. Arnoux, V. Berthé, Z. Masáková and E. Pelantová, Sturm numbers and substitution invariance of 3iet words. Integers 8 (2008) 17 (electronic). | Zbl

[4] P. Baláži, Z. Masáková and E. Pelantová, Complete characterization of substitution invariant Sturmian sequences. Integers 5 (2005) 23 (electronic). | Zbl

[5] P. Baláži, Z. Masáková and E. Pelantová, Characterization of substitution invariant 3iet words. Integers 8 (2008) 21 (electronic).

[6] J. Berstel and P. Séébold, Morphismes de Sturm. Bull. Belg. Math. Soc. Simon Stevin 1 (1994) 175-189. Journées Montoises (Mons, 1992). | Zbl

[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. | Numdam | Zbl

[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. | Zbl

[9] D. Crisp, W. Moran, A. Pollington and P. Shiue, Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux 5 (1993) 123-137. | Numdam | Zbl

[10] S. Ferenczi, C. Holton and L.Q. Zamboni, Structure of three interval exchange transformations. I. An arithmetic study. Ann. Inst. Fourier 51 (2001) 861-901. | Numdam | Zbl

[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. | Zbl

[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. | Zbl

[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. | Zbl

[14] T. Komatsu and A.J. Van Der Poorten, Substitution invariant Beatty sequences. Jpn J. Math. (N.S.) 22 (1996) 349-354. | Zbl

[15] F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux 5 (1993) 221-233. | Numdam | Zbl

[16] B. Parvaix, Substitution invariant Sturmian bisequences. J. Théor. Nombres Bordeaux 11 (1999) 201-210. Les XXèmes Journées Arithmétiques (Limoges, 1997). | Numdam | Zbl

[17] M. Queffélec, Substitution dynamical systems-spectral analysis. Lect. Notes Math. 1294 (1987). | Zbl

[18] P. Séébold, Fibonacci morphisms and Sturmian words. Theoret. Comput. Sci. 88 (1991) 365-384. | Zbl

[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. | Zbl

Cité par Sources :