Substitution invariant sturmian bisequences

Bruno Parvaix

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 1, page 201-210
  • ISSN: 1246-7405

Abstract

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We prove that a Sturmian bisequence, with slope α and intercept ρ , is fixed by some non-trivial substitution if and only if α is a Sturm number and ρ belongs to ℚ ( α ) . We also detail a complementary system of integers connected with Beatty bisequences.

How to cite

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Parvaix, Bruno. "Substitution invariant sturmian bisequences." Journal de théorie des nombres de Bordeaux 11.1 (1999): 201-210. <http://eudml.org/doc/248339>.

@article{Parvaix1999,
abstract = {We prove that a Sturmian bisequence, with slope $\alpha $ and intercept $\rho $, is fixed by some non-trivial substitution if and only if $\alpha $ is a Sturm number and $\rho $ belongs to $\mathbb \{Q\}(\alpha )$. We also detail a complementary system of integers connected with Beatty bisequences.},
author = {Parvaix, Bruno},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Beatty sequences; Sturmian bisequences; Sturmian sequences; Sturmian number},
language = {eng},
number = {1},
pages = {201-210},
publisher = {Université Bordeaux I},
title = {Substitution invariant sturmian bisequences},
url = {http://eudml.org/doc/248339},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Parvaix, Bruno
TI - Substitution invariant sturmian bisequences
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 1
SP - 201
EP - 210
AB - We prove that a Sturmian bisequence, with slope $\alpha $ and intercept $\rho $, is fixed by some non-trivial substitution if and only if $\alpha $ is a Sturm number and $\rho $ belongs to $\mathbb {Q}(\alpha )$. We also detail a complementary system of integers connected with Beatty bisequences.
LA - eng
KW - Beatty sequences; Sturmian bisequences; Sturmian sequences; Sturmian number
UR - http://eudml.org/doc/248339
ER -

References

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Citations in EuDML Documents

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  1. P. Dartnell, F. Durand, A. Maass, Orbit equivalence and Kakutani equivalence with Sturmian subshifts
  2. Petr Ambrož, Zuzana Masáková, Edita Pelantová, Christiane Frougny, Palindromic complexity of infinite words associated with simple Parry numbers
  3. Valérie Berthé, Hiromi Ei, Shunji Ito, Hui Rao, On substitution invariant Sturmian words: an application of Rauzy fractals
  4. Petr Ambrož, Zuzana Masáková, Edita Pelantová, Morphisms fixing words associated with exchange of three intervals

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