Reference : Syndeticity and independent substitutions
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Engineering, computing & technology : Computer science
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Syndeticity and independent substitutions
Durand, Fabien [ > > ]
Rigo, Michel mailto [Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes >]
Advances in Applied Mathematics
Academic Press
Yes (verified by ORBi)
[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.

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