A Succinct Study of Positionality for Dumont--Thomas Numeration Systems

[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.

Disciplines :

Mathematics

Author, co-author :

Kreczman, Savinien ; Université de Liège - ULiège > Mathematics

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 :

2025

Event name :

15th International Conference on WORDS

Event date :

30/06--04/07

Audience :

International

Journal title :

Lecture Notes in Computer Science

ISSN :

0302-9743

eISSN :

1611-3349

Publisher :

Springer, Cham, Switzerland

Volume :

15729

Pages :

179–191

Peer review/Selection committee :

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.

Commentary :

12 pages

Available on ORBi :

since 11 June 2025

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Bibliography

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