Auto-similarity in Rational Base Number Systems - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2013

Auto-similarity in Rational Base Number Systems

Résumé

This work is a contribution to the study of set of the representa-tions of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the integers and whose subtrees are all distinct. With every node of that tree is then associated a minimal infinite word. The main result is that a sequential transducer which computes for all n the minimal word associated with n + 1 from the one asso-ciated with n, has essentially the same underlying graph as the tree itself. These infinite words are then interpreted as representations of real numbers; the difference between the numbers represented by these two consecutive minimal words is the called the span of a node of the tree. The preceding construction allows to characterise the topological closure of the set of spans.
Fichier principal
Vignette du fichier
1305.6757v1.pdf (295.46 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01075822 , version 1 (20-10-2014)

Identifiants

Citer

Shigeki Akiyama, Victor Marsault, Jacques Sakarovitch. Auto-similarity in Rational Base Number Systems. 2014. ⟨hal-01075822⟩
80 Consultations
35 Téléchargements

Altmetric

Partager

More