Reference : Automatic sequences: from rational bases to trees
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Physical, chemical, mathematical & earth Sciences : Mathematics
Automatic sequences: from rational bases to trees
Rigo, Michel mailto [Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes >]
Stipulanti, Manon mailto [Université de Liège - ULiège > Département de mathématique > Département de mathématique >]
[en] Automatic sequences ; abstract numeration systems ; ational base numeration systems ; alternating morphisms ; PD0L systems ; Cobham’s theorem.
[en] The nth term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of n in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration system with a regular numeration language, we consider these built on languages associated with trees having periodic labeled signatures and, in particular, rational base numeration systems. We obtain two main characterizations of these sequences. The first one is concerned with r-block substitutions where r morphisms are applied periodically. In particular, we provide examples of such sequences that are not morphic. The second characterization involves the factors, or subtrees of finite height, of the tree associated with the numeration system and decorated by the terms of the sequence.
F.R.S.-FNRS - Fonds de la Recherche Scientifique
Researchers ; Professionals ; Students

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