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
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
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