Substitutions with Cofinal Fixed Points

TAN, Bo; WEN, Zhi-Xiong; WU, Jun; WEN, Zhi-Ying

doi:10.5802/aif.2249

Substitutions with Cofinal Fixed Points
[Substitutions de Points fixes co-finaux]

TAN, Bo ¹ ; WEN, Zhi-Xiong ¹ ; WU, Jun ¹ ; WEN, Zhi-Ying ²

¹ Huazhong University of Science and Technology Department of Mathematics Wuhan, 430074 (P.R. China)
² Tsinghua University Department of Mathematics Beijing, 100084 (P.R. China)

Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2551-2563.

Résumé
Abstract

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.

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.

MR Zbl

DOI : 10.5802/aif.2249

Classification : 68R15, 11B85
Keywords: Cofinal sequences, substitution
Mot clés : Suites co-finales, substitution

Affiliations des auteurs :

TAN, Bo ¹ ; WEN, Zhi-Xiong ¹ ; WU, Jun ¹ ; WEN, Zhi-Ying ²

¹ Huazhong University of Science and Technology Department of Mathematics Wuhan, 430074 (P.R. China)
² Tsinghua University Department of Mathematics Beijing, 100084 (P.R. China)

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     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},
     pages = {2551--2563},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {56},
     number = {7},
     year = {2006},
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     zbl = {1121.68092},
     mrnumber = {2290790},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2249/}
}

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TAN, Bo; WEN, Zhi-Xiong; WU, Jun; WEN, Zhi-Ying. Substitutions with Cofinal Fixed Points. Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2551-2563. doi : 10.5802/aif.2249. http://archive.numdam.org/articles/10.5802/aif.2249/

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