Primitive substitutive numbers are closed under rational multiplication

Pallavi Ketkar; Luca Q. Zamboni

Journal de théorie des nombres de Bordeaux (1998)

  • Volume: 10, Issue: 2, page 315-320
  • ISSN: 1246-7405

Abstract

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Let M ( r ) denote the set of real numbers α 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 ( r ) is closed under multiplication by rational numbers, but not closed under addition.

How to cite

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Ketkar, Pallavi, and Zamboni, Luca Q.. "Primitive substitutive numbers are closed under rational multiplication." Journal de théorie des nombres de Bordeaux 10.2 (1998): 315-320. <http://eudml.org/doc/248170>.

@article{Ketkar1998,
abstract = {Let $M(r)$ 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 $M(r)$ is closed under multiplication by rational numbers, but not closed under addition.},
author = {Ketkar, Pallavi, Zamboni, Luca Q.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {substitutive real numbers; automatic real numbers},
language = {eng},
number = {2},
pages = {315-320},
publisher = {Université Bordeaux I},
title = {Primitive substitutive numbers are closed under rational multiplication},
url = {http://eudml.org/doc/248170},
volume = {10},
year = {1998},
}

TY - JOUR
AU - Ketkar, Pallavi
AU - Zamboni, Luca Q.
TI - Primitive substitutive numbers are closed under rational multiplication
JO - Journal de théorie des nombres de Bordeaux
PY - 1998
PB - Université Bordeaux I
VL - 10
IS - 2
SP - 315
EP - 320
AB - Let $M(r)$ 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 $M(r)$ is closed under multiplication by rational numbers, but not closed under addition.
LA - eng
KW - substitutive real numbers; automatic real numbers
UR - http://eudml.org/doc/248170
ER -

References

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