Morphismes sturmiens et règles de Rauzy
Journal de Théorie des Nombres de Bordeaux, Volume 5 (1993) no. 2, pp. 221-233.

We give a complete characterization of binary morphisms which preserve Sturmian words and show that infinite words generated by these morphisms are rigid.

Nous donnons une caractérisation complète de tous les morphismes binaires qui préservent les mots sturmiens et montrons que les mots infinis engendrés par ces morphismes sont rigides.

@article{JTNB_1993__5_2_221_0,
     author = {Filippo Mignosi and Patrice S\'e\'ebold},
     title = {Morphismes sturmiens et r\`egles de {Rauzy}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {221--233},
     publisher = {Universit\'e Bordeaux I},
     volume = {5},
     number = {2},
     year = {1993},
     doi = {10.5802/jtnb.91},
     zbl = {0797.11029},
     mrnumber = {1265903},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.91/}
}
TY  - JOUR
TI  - Morphismes sturmiens et règles de Rauzy
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 1993
DA  - 1993///
SP  - 221
EP  - 233
VL  - 5
IS  - 2
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.91/
UR  - https://zbmath.org/?q=an%3A0797.11029
UR  - https://www.ams.org/mathscinet-getitem?mr=1265903
UR  - https://doi.org/10.5802/jtnb.91
DO  - 10.5802/jtnb.91
LA  - fr
ID  - JTNB_1993__5_2_221_0
ER  - 
%0 Journal Article
%T Morphismes sturmiens et règles de Rauzy
%J Journal de Théorie des Nombres de Bordeaux
%D 1993
%P 221-233
%V 5
%N 2
%I Université Bordeaux I
%U https://doi.org/10.5802/jtnb.91
%R 10.5802/jtnb.91
%G fr
%F JTNB_1993__5_2_221_0
Filippo Mignosi; Patrice Séébold. Morphismes sturmiens et règles de Rauzy. Journal de Théorie des Nombres de Bordeaux, Volume 5 (1993) no. 2, pp. 221-233. doi : 10.5802/jtnb.91. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.91/

[1] T.C. Brown, A characterization of the quadratic irrationals, Canad. Math. Bull. 34 (1991), 36-41. | MR: 1108926 | Zbl: 0688.10007

[2] D. Crisp, W. Moran, A. Pollington, P. Shiue, Substitution invariant cutting sequences, Journal de Théorie des Nombres de Bordeaux 5 (1993), 123-137. | Numdam | MR: 1251232 | Zbl: 0786.11041

[3] E. Coven, G.A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138-153. | MR: 322838 | Zbl: 0256.54028

[4] S. Dulucq, D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400. | MR: 1057771 | Zbl: 0694.68048

[5] A.S. Fraenkel, M. Mushkin, U. Tassa, Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. | Zbl: 0401.10018

[6] G.A. Hedlund, Sturmian minimal sets, Amer. J. Math 66 (1944), 605-620. | MR: 10792 | Zbl: 0063.01982

[7] G.A. Hedlund, M. Morse, Symbolic dynamics II - Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42. | JFM: 66.0188.03 | MR: 745 | Zbl: 0022.34003

[8] S. Ito, S. Yasutomi, On continued fractions, substitutions and characteristic sequences, Japan. J. Math. 16 (1990), 287-306. | MR: 1091163 | Zbl: 0721.11009

[9] M. Kósa, Problems 149-151, "Problems and Solutions", EATCS Bulletin 32 (1987), 331-333.

[10] M. Lothaire, Combinatorics on words, Addison Wesley, 1982. | MR: 675953 | Zbl: 0514.20045

[11] F. Mignosi, On the number of factors of Sturmian words, Theoret. Comput. Sci. 82 (1991), 71-84. | MR: 1112109 | Zbl: 0728.68093

[12] G. Rauzy, Mots infinis en arithmétique, in Automata on infinite words, Nivat, Perrin (Eds), Lecture Notes in Computer Science, Springer-Verlag 192 (1984), 165-171. | MR: 814741 | Zbl: 0613.10044

[13] P. Séébold, Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci. 88 (1991), 365-384. | MR: 1131075 | Zbl: 0737.68068

[14] C. Series, The geometry of Markoff numbers, Math. Intelligencer 7 (1985), 20-29. | MR: 795536 | Zbl: 0566.10024

[15] K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR: 444558 | Zbl: 0359.10028

[16] B.A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. | MR: 265267 | Zbl: 0204.37101

Cited by Sources: