Cobham's theorem for substitutions

Durand, Fabien. "Cobham's theorem for substitutions." Journal of the European Mathematical Society 013.6 (2011): 1799-1814. <http://eudml.org/doc/277320>.

@article{Durand2011,
abstract = {The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let $\alpha $ and $\beta $ be two multiplicatively independent Perron numbers. Then a sequence $x\in A^\{\mathbb \{N\}\}$, where $A$ is a finite alphabet, is both $\alpha $-substitutive and $\beta $-substitutive if and only if $x$ is ultimately periodic.},
author = {Durand, Fabien},
journal = {Journal of the European Mathematical Society},
keywords = {Cobham's theorem; substitutive sequence; return words; Cobham's theorem; Cobham's theorem; substitutive sequence; return words},
language = {eng},
number = {6},
pages = {1799-1814},
publisher = {European Mathematical Society Publishing House},
title = {Cobham's theorem for substitutions},
url = {http://eudml.org/doc/277320},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Durand, Fabien
TI - Cobham's theorem for substitutions
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 6
SP - 1799
EP - 1814
AB - The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let $\alpha $ and $\beta $ be two multiplicatively independent Perron numbers. Then a sequence $x\in A^{\mathbb {N}}$, where $A$ is a finite alphabet, is both $\alpha $-substitutive and $\beta $-substitutive if and only if $x$ is ultimately periodic.
LA - eng
KW - Cobham's theorem; substitutive sequence; return words; Cobham's theorem; Cobham's theorem; substitutive sequence; return words
UR - http://eudml.org/doc/277320
ER -