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Automatic sequences in rational base numeration systems (and even more)
Stipulanti, Manon
2021Discrete Math. Seminar
 

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Keywords :
automatic sequences; abstract numeration systems; rational base numeration systems; alternating morphisms; PD0L systems; Cobham's theorem; factor complexity
Abstract :
[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. Here, 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.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon  ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Language :
English
Title :
Automatic sequences in rational base numeration systems (and even more)
Publication date :
31 March 2021
Number of pages :
41
Event name :
Discrete Math. Seminar
Event organizer :
Université de Liège
Event place :
Liège, Belgium
Event date :
de septembre 2020 à juillet 2021
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Commentary :
Work in collaboration with Michel Rigo (ULiège, m.rigo@uliege.be). // Travail en collaboration avec Michel Rigo (ULiège, m.rigo@uliege.be).
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since 31 March 2021

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