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.
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.
@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}, zbl = {0978.11005}, mrnumber = {1730440}, language = {en}, url = {http://www.numdam.org/item/JTNB_1999__11_1_201_0/} }
TY - JOUR AU - Parvaix, Bruno TI - Substitution invariant sturmian bisequences JO - Journal de Théorie des Nombres de Bordeaux PY - 1999 DA - 1999/// SP - 201 EP - 210 VL - 11 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1999__11_1_201_0/ UR - https://zbmath.org/?q=an%3A0978.11005 UR - https://www.ams.org/mathscinet-getitem?mr=1730440 LA - en ID - JTNB_1999__11_1_201_0 ER -
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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