Real numbers having ultimately periodic representations in abstract numeration systems

Lecomte, Pierre; Rigo, Michel

doi:10.1016/j.ic.2003.12.006

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Article (Scientific journals)

Real numbers having ultimately periodic representations in abstract numeration systems

Lecomte, Pierre; Rigo, Michel

2004 • In Information and Computation, 192 (1), p. 57-83

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https://hdl.handle.net/2268/15825

DOI
10.1016/j.ic.2003.12.006

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Keywords :

numeration system; regular language; representation of real numbers; ultimately periodic word

Abstract :

[en] Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words are also investigated. Finally, we show the equivalence of the classical theta-expansions with our generalized representations in some special case related to a Pisot number theta. (C) 2004 Elsevier Inc. All rights reserved.

Disciplines :

Mathematics
Computer science

Author, co-author :

Lecomte, Pierre ; Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes

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

Language :

English

Title :

Real numbers having ultimately periodic representations in abstract numeration systems

Publication date :

01 July 2004

Journal title :

Information and Computation

ISSN :

0890-5401

eISSN :

1090-2651

Publisher :

Academic Press Inc Elsevier Science, San Diego, United States - California

Volume :

192

Issue :

Pages :

57-83

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 01 July 2009

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