# Cobham's theorem for substitutions

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 6, page 1799-1814
- ISSN: 1435-9855

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topDurand, 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 -

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