Geodesic
A Generalization of Cobham's Theorem for Regular Sequences
Séminaire lotharingien de combinatoire, 54A (2005-2007)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A sequence is said to be k-automatic if the nth term of this sequence is generated by a finite state machine with n in base k as input. A result due to Cobham states that if a sequence is both k- andl-automatic and k and l are multiplicatively independent, then the sequence is eventually periodic. Allouche and Shallit defined (R,k)-regular sequences as a natural generalization of k-automatic sequences for a given ring R. In this paper we prove the following generalization of Cobham's theorem: If a sequence is (R,k)- and (R,l)-regular and k and l are multiplicatively independent, then the sequence satisfies a linear recurrence over R. 

@article{SLC_2005-2007_54A_a15,
     author = {Jason P. Bell},
     title = {A {Generalization} of {Cobham's} {Theorem} for {Regular} {Sequences}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {54A},
     year = {2005-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a15/}
}
TY  - JOUR
AU  - Jason P. Bell
TI  - A Generalization of Cobham's Theorem for Regular Sequences
JO  - Séminaire lotharingien de combinatoire
PY  - 2005-2007
VL  - 54A
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a15/
ID  - SLC_2005-2007_54A_a15
ER  - 
%0 Journal Article
%A Jason P. Bell
%T A Generalization of Cobham's Theorem for Regular Sequences
%J Séminaire lotharingien de combinatoire
%D 2005-2007
%V 54A
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a15/
%F SLC_2005-2007_54A_a15
Jason P. Bell. A Generalization of Cobham's Theorem for Regular Sequences. Séminaire lotharingien de combinatoire, 54A (2005-2007). http://geodesic.mathdoc.fr/item/SLC_2005-2007_54A_a15/