Automatic sequences: from rational bases to trees

Rigo, Michel; Stipulanti, Manon

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Automatic sequences: from rational bases to trees

Rigo, Michel; Stipulanti, Manon

2021 • In Discrete Mathematics and Theoretical Computer Science, 24 (1), p. 25

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Keywords :

Automatic sequences; abstract numeration systems; ational base numeration systems; alternating morphisms; PD0L systems; Cobham’s theorem.

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. 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.

Disciplines :

Mathematics

Author, co-author :

Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Département de mathématique

Language :

English

Title :

Automatic sequences: from rational bases to trees

Publication date :

2021

Journal title :

Discrete Mathematics and Theoretical Computer Science

ISSN :

1365-8050

eISSN :

1462-7264

Publisher :

Maison de l'informatique et des mathematiques discretes, France

Volume :

Issue :

Pages :

Paper 25

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 23 February 2021

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