Reference : Syndeticity and independent substitutions
Scientific journals : Article
Engineering, computing & technology : Computer science
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/15908
Syndeticity and independent substitutions
English
Durand, Fabien [ > > ]
Rigo, Michel mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
2009
Advances in Applied Mathematics
Academic Press
42
1-22
Yes (verified by ORBi)
International
0196-8858
[en] Syndeticity ; Morphism ; Cobham's theorem ; Abstract numeration system ; Regular language ; Substitution
[en] We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we de ne the notion of two independent substitutions. Our
main result is the following. If a sequence x is generated by two independent substitutions, at least one being of exponential growth, then the factors of x appearing in nitely often in x appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential.
Researchers
http://hdl.handle.net/2268/15908
10.1016/j.aam.2008.02.001

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