Let denote the set of real numbers whose base- digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set is closed under multiplication by rational numbers, but not closed under addition.
Soit l’ensemble des réels dont le développement en base contient une queue qui est l’image d’un point fixe d’une substitution primitive par un morphisme de lettres. Nous démontrons que l’ensemble est stable par multiplication par les rationnels, mais non stable par addition.
@article{JTNB_1998__10_2_315_0, author = {Pallavi Ketkar and Luca Q. Zamboni}, title = {Primitive substitutive numbers are closed under rational multiplication}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {315--320}, publisher = {Universit\'e Bordeaux I}, volume = {10}, number = {2}, year = {1998}, doi = {10.5802/jtnb.231}, zbl = {0930.11008}, mrnumber = {1828248}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.231/} }
TY - JOUR TI - Primitive substitutive numbers are closed under rational multiplication JO - Journal de Théorie des Nombres de Bordeaux PY - 1998 DA - 1998/// SP - 315 EP - 320 VL - 10 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.231/ UR - https://zbmath.org/?q=an%3A0930.11008 UR - https://www.ams.org/mathscinet-getitem?mr=1828248 UR - https://doi.org/10.5802/jtnb.231 DO - 10.5802/jtnb.231 LA - en ID - JTNB_1998__10_2_315_0 ER -
Pallavi Ketkar; Luca Q. Zamboni. Primitive substitutive numbers are closed under rational multiplication. Journal de Théorie des Nombres de Bordeaux, Volume 10 (1998) no. 2, pp. 315-320. doi : 10.5802/jtnb.231. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.231/
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