On invertible substitutions with two fixed points

Zhi-Xiong Wen; Zhi-Ying Wen; Jun Wu

doi:10.1016/S1631-073X(02)02235-5

On invertible substitutions with two fixed points
[Sur les substitutions inversibles ayant deux points fixes]

Zhi-Xiong Wen ¹ ; Zhi-Ying Wen ² ; Jun Wu ¹

¹ Nonlinear Science Center, Department of Mathematics, Wuhan University, Wuhan 430072, China
² Department of Mathematics, Tsinghua University, Beijing 10084, China

Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 727-731.

Résumé
Abstract

On considère une substitution primitive ϕ sur l'alphabet {a,b} ayant deux points fixes ξ_a et ξ_b (commençant respectivement par a et b). Nous montrons que la substitution ϕ est inversible si et seulement si l'on a ξ_a=abξ et ξ_b=baξ.

Let ϕ be a primitive substitution on a two-letter alphabet {a,b} having two fixed points ξ_a and ξ_b. We show that the substitution ϕ is invertible if and only if one has ξ_a=abξ and ξ_b=baξ.

Reçu le : 2001-10-24
Accepté le : 2001-12-03
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02235-5

Affiliations des auteurs :

Zhi-Xiong Wen ¹ ; Zhi-Ying Wen ² ; Jun Wu ¹

¹ Nonlinear Science Center, Department of Mathematics, Wuhan University, Wuhan 430072, China
² Department of Mathematics, Tsinghua University, Beijing 10084, China

@article{CRMATH_2002__334_9_727_0,
     author = {Zhi-Xiong Wen and Zhi-Ying Wen and Jun Wu},
     title = {On invertible substitutions with two fixed points},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {727--731},
     publisher = {Elsevier},
     volume = {334},
     number = {9},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02235-5},
     language = {en},
}

TY  - JOUR
AU  - Zhi-Xiong Wen
AU  - Zhi-Ying Wen
AU  - Jun Wu
TI  - On invertible substitutions with two fixed points
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 727
EP  - 731
VL  - 334
IS  - 9
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02235-5
LA  - en
ID  - CRMATH_2002__334_9_727_0
ER  -

%0 Journal Article
%A Zhi-Xiong Wen
%A Zhi-Ying Wen
%A Jun Wu
%T On invertible substitutions with two fixed points
%J Comptes Rendus. Mathématique
%D 2002
%P 727-731
%V 334
%N 9
%I Elsevier
%R 10.1016/S1631-073X(02)02235-5
%G en
%F CRMATH_2002__334_9_727_0

Zhi-Xiong Wen; Zhi-Ying Wen; Jun Wu. On invertible substitutions with two fixed points. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 727-731. doi : 10.1016/S1631-073X(02)02235-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02235-5/

Bibliographie
Cité par

[1] Berstel J., Mot de Fibonacci, Séminaire d'informatique théorique, L.I.T.P., Paris, Année (1980/1981) 57–78

[2] H. Ei; S. Ito Decomposition theorem for invertible substitution, Osaka J. Math., Volume 34 (1998), pp. 821-834

[3] Mignosi F., Ph.D. thesis, L.I.T.P., 92.01

[4] F. Mignosi; P. Séébold Morphismes sturmiens et règles de Rauzy, J. Théorie des Nombres de Bordeaux, Volume 5 (1993), pp. 221-233

[5] J. Nielsen Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden, Math. Ann., Volume 78 (1918), pp. 385-397

[6] P. Séébold Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci., Volume 88 (1991), pp. 365-384

[7] Z.-X. Wen; Z.-Y. Wen Local isomorphism of the invertible substitutions, C. R. Acad. Sci. Paris, Série I, Volume 318 (1994), pp. 299-304

[8] Z.-X. Wen; Z.-Y. Wen Some properties of the singular words of the Fibonacci word, European J. Combin., Volume 15 (1994), pp. 587-598

[9] Z.-X. Wen; Z.-Y. Wen Factor properties of infinite words generated by a class of invertible substitution, 5th Conference Formal Power Series and Algebraic Combinatorics, Florence, 1993, pp. 455-466

[10] Wen Z.-X., Wen Z.-Y., Wu J., Some properties of Fibonacci sequence, Preprint

Cité par Sources :

^☆ Supported by the Special Funds for Major State Basic Research Projects of China and Morningside Center of Mathematics (CAS).

Commentaires - Politique