We prove that a Sturmian bisequence, with slope and intercept , is fixed by some non-trivial substitution if and only if is a Sturm number and belongs to . We also detail a complementary system of integers connected with Beatty bisequences.
Les suites sturmiennes indexées sur , de pente et d’intercept , sont laissées fixes par une substitution non triviale si et seulement si est un nombre de Sturm et appartient à . 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}, pages = {201--210}, publisher = {Universit\'e Bordeaux I}, volume = {11}, number = {1}, year = {1999}, mrnumber = {1730440}, zbl = {0978.11005}, 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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