Substitution invariant sturmian bisequences

Bruno Parvaix

Bruno Parvaix

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

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     title = {Substitution invariant sturmian bisequences},
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     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {1},
     year = {1999},
     zbl = {0978.11005},
     mrnumber = {1730440},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_201_0/}
}

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

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