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

Bruno Parvaix. Substitution invariant sturmian bisequences. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 201-210. doi: 10.5802/jtnb.246
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