Article (Scientific journals)
Abstract numeration systems on bounded languages and multiplication by a constant
Charlier, Emilie; Rigo, Michel; Steiner, Wolfgang
2008In Integers, 8 (1-A35), p. 1-19
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Keywords :
numeration system; recognizable sets of integers; bounded language; multiplication by a constant; combinatorial numeration system
Abstract :
[en] A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $\lambda\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $\lambda X$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system.
Disciplines :
Computer science
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Steiner, Wolfgang
Language :
English
Title :
Abstract numeration systems on bounded languages and multiplication by a constant
Publication date :
2008
Journal title :
Integers
eISSN :
1553-1732
Publisher :
Integers, Carrollton, United States - Georgia
Volume :
8
Issue :
1-A35
Pages :
1-19
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 01 July 2009

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