Substitutions with Cofinal Fixed Points
Annales de l'Institut Fourier, Volume 56 (2006) no. 7, p. 2551-2563

Let ϕ be a substitution over a 2-letter alphabet, say {a,b}. If ϕ(a) and ϕ(b) begin with a and b respectively, ϕ has two fixed points beginning with a and b respectively.

We characterize substitutions with two cofinal fixed points (i.e., which differ only by prefixes). The proof is a combinatorial one, based on the study of repetitions of words in the fixed points.

Soit ϕ une substitution en un alphabet {a,b} de deux lettres. Si ϕ(a) et ϕ(b) commencent par a et b respectivement, alors ϕ possède deux points fixes débutants par a et b respectivement.

Nous caractériserons les substitutions avec deux points fixes co-finaux (c’est-à-dire, qui diffèrent que par leur préfixe). La démonstration est combinatoire, elle se base sur une étude de répétitions de mots dans les points fixes.

DOI : https://doi.org/10.5802/aif.2249
Classification:  68R15,  11B85
Keywords: Cofinal sequences, substitution
@article{AIF_2006__56_7_2551_0,
     author = {TAN, Bo and WEN, Zhi-Xiong and WU, Jun and WEN, Zhi-Ying},
     title = {Substitutions with Cofinal Fixed Points},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {7},
     year = {2006},
     pages = {2551-2563},
     doi = {10.5802/aif.2249},
     mrnumber = {2290790},
     zbl = {1121.68092},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_7_2551_0}
}
TAN, Bo; WEN, Zhi-Xiong; WU, Jun; WEN, Zhi-Ying. Substitutions with Cofinal Fixed Points. Annales de l'Institut Fourier, Volume 56 (2006) no. 7, pp. 2551-2563. doi : 10.5802/aif.2249. http://www.numdam.org/item/AIF_2006__56_7_2551_0/

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