Substitution invariant sturmian bisequences

Parvaix, Bruno

Parvaix, Bruno

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

Résumé
Abstract

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.

MR Zbl | 3 citations dans Numdam

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     url = {http://www.numdam.org/item/JTNB_1999__11_1_201_0/}
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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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