[en] Numeration systems are maps between a set of numbers and a set of words that act as representations of these numbers. One desirable property is positionality: the ability to relate positions in the words to values of the numbers. In general, positionality is hard to decide. In this article, we obtain a criterion to decide the positionality of so-called Dumont–Thomas numeration systems, arising from substitutions. Then, we particularize this criterion to some well-behaved classes of substitutions, allowing us to link the related systems to existing literature.
Labbé, Sébastien; Université de Bordeaux > Laboratoire Bordelais de Recherche en Informatique
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
A Succinct Study of Positionality for Dumont--Thomas Numeration Systems
Publication date :
In press
Journal title :
Lecture Notes in Computer Science
ISSN :
0302-9743
eISSN :
1611-3349
Publisher :
Springer, Cham, Switzerland
Special issue title :
Combinatorics on Words
Peer reviewed :
Peer reviewed
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique ANR - Agence Nationale de la Recherche
Funding text :
Savinien Kreczman : soutenu par le FNRS, Research Fellow Grant 1.A.789.23F. Sébastien Labbé : soutenu par l'ANR, projet IZES (ANR-22-CE40-0011). Manon Stipulanti : soutenue par le FNRS, Research grant 1.C.104.24F.
