Substitutions with Cofinal Fixed Points

Bo TAN[1]; Zhi-Xiong WEN[1]; Jun WU[1]; Zhi-Ying WEN[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 (2006)

  • Volume: 56, Issue: 7, page 2551-2563
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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TAN, Bo, et al. "Substitutions with Cofinal Fixed Points." Annales de l’institut Fourier 56.7 (2006): 2551-2563. <http://eudml.org/doc/10213>.

@article{TAN2006,
abstract = {Let $\varphi $ be a substitution over a 2-letter alphabet, say $\lbrace a, b\rbrace $. If $\varphi (a)$ and $\varphi (b)$ begin with $a$ and $b$ respectively, $\varphi $ 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.},
affiliation = {Huazhong University of Science and Technology Department of Mathematics Wuhan, 430074 (P.R. China); Huazhong University of Science and Technology Department of Mathematics Wuhan, 430074 (P.R. China); Huazhong University of Science and Technology Department of Mathematics Wuhan, 430074 (P.R. China); Tsinghua University Department of Mathematics Beijing, 100084 (P.R. China)},
author = {TAN, Bo, WEN, Zhi-Xiong, WU, Jun, WEN, Zhi-Ying},
journal = {Annales de l’institut Fourier},
keywords = {Cofinal sequences; substitution; cofinal sequences},
language = {eng},
number = {7},
pages = {2551-2563},
publisher = {Association des Annales de l’institut Fourier},
title = {Substitutions with Cofinal Fixed Points},
url = {http://eudml.org/doc/10213},
volume = {56},
year = {2006},
}

TY - JOUR
AU - TAN, Bo
AU - WEN, Zhi-Xiong
AU - WU, Jun
AU - WEN, Zhi-Ying
TI - Substitutions with Cofinal Fixed Points
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 7
SP - 2551
EP - 2563
AB - Let $\varphi $ be a substitution over a 2-letter alphabet, say $\lbrace a, b\rbrace $. If $\varphi (a)$ and $\varphi (b)$ begin with $a$ and $b$ respectively, $\varphi $ 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.
LA - eng
KW - Cofinal sequences; substitution; cofinal sequences
UR - http://eudml.org/doc/10213
ER -

References

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  11. B. Tan, Z.-X. Wen, Y. P. Zhang, The structure of invertible substitutions on a three-letter alphabet, Adv. in Appl. Math. 32 (2004), 736-753 Zbl1082.68092MR2053843
  12. Z.-X. Wen, Z.-Y. Wen, Local isomorphism of the invertible substitutions, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), 299-304 Zbl0812.11018MR1267604
  13. Z.-X. Wen, Z.-Y. Wen, J. Wu, On invertible substitutions with two fixed points, C. R. Math. Acad. Sci. Paris 334 (2002), 727-731 Zbl0996.68149MR1905029
  14. Z.-X. Wen, Y. P. Zhang, Some remarks on invertible substitutions on three letter alphabet, Chinese Sci. Bull. 44 (1999), 1755-1760 Zbl1040.20504MR1737516

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