Reference : Conservation du caractère reconnaissable par opérations arithmétiques dans un système de...

	Document type :	Dissertations and theses : Master of advanced studies dissertation
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/2268/8808

Title :	Conservation du caractère reconnaissable par opérations arithmétiques dans un système de numération abstrait
Language :	French
Alternative title :	[en] Preservation of recognizability under arithmetic operations in an abstract numeration system
Author, co-author :	Charlier, Emilie [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
Publication date :	29-Jun-2006
Institution :	Université de Liège
Name of the degree :	dipômé d'études appronfondies en sciences
Page number :	vi, 61
City :	Liège
Country :	Belgium
Superviser :	Rigo, Michel
Member of the jury :	Wolper, Pierre
	Hansoul, Georges
	Lecomte, Pierre
Abstract :	[en] In this thesis, I study the stability of recognizability under arithmetic operations like addition, multiplication by a constant or multiplication, in an abstract numeration system. The main result presented in this work concerns the abstract numeration system built on the bounded language a^*b^*. It shows that, in this case, multiplication by a constant preserves recognizability if and only if this constant is an odd square. I end this text by providing some partial results of a generalization to abstract numeration system built on any bounded language.
Permalink :	http://hdl.handle.net/2268/8808

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