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

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.

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.

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

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