Reference : Conservation du caractère reconnaissable par opérations arithmétiques dans un système...
Dissertations and theses : Master of advanced studies dissertation
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/8808
Conservation du caractère reconnaissable par opérations arithmétiques dans un système de numération abstrait
French
[en] Preservation of recognizability under arithmetic operations in an abstract numeration system
Charlier, Emilie mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
29-Jun-2006
Université de Liège, ​Liège, ​​Belgium
dipômé d'études appronfondies en sciences
vi, 61
Rigo, Michel mailto
Wolper, Pierre mailto
Hansoul, Georges mailto
Lecomte, Pierre mailto
[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.
http://hdl.handle.net/2268/8808

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