Primitive substitutive numbers are closed under rational multiplication
Journal de Théorie des Nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 315-320.

Soit $M\left(r\right)$ l’ensemble des réels $\alpha$ dont le développement en base $r$ 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 $M\left(r\right)$ est stable par multiplication par les rationnels, mais non stable par addition.

Let $M\left(r\right)$ denote the set of real numbers $\alpha$ whose base-$r$ 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 $M\left(r\right)$ is closed under multiplication by rational numbers, but not closed under addition.

@article{JTNB_1998__10_2_315_0,
author = {Ketkar, Pallavi and Zamboni, Luca Q.},
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 = {jtnb.centre-mersenne.org/item/JTNB_1998__10_2_315_0/}
}
Pallavi Ketkar; Luca Q. Zamboni. Primitive substitutive numbers are closed under rational multiplication. Journal de Théorie des Nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 315-320. doi : 10.5802/jtnb.231. https://jtnb.centre-mersenne.org/item/JTNB_1998__10_2_315_0/

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