Substitution invariant sturmian bisequences
Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, p. 201-210

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.

Les suites sturmiennes indexées sur ℤ, de pente α et d’intercept ρ, sont laissées fixes par une substitution non triviale si et seulement si α est un nombre de Sturm et ρ appartient à ℚ(α). On remarque aussi que les suites de Beatty permettent de définir des partitions de l’ensemble des entiers relatifs.

@article{JTNB_1999__11_1_201_0,
     author = {Parvaix, Bruno},
     title = {Substitution invariant sturmian bisequences},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {1},
     year = {1999},
     pages = {201-210},
     zbl = {0978.11005},
     mrnumber = {1730440},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1999__11_1_201_0}
}

Parvaix, Bruno. Substitution invariant sturmian bisequences. Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 201-210. http://www.numdam.org/item/JTNB_1999__11_1_201_0/

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