Reference : Multidimensional generalized automatic sequences and shape-symmetric morphic words
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
http://hdl.handle.net/2268/32179
Multidimensional generalized automatic sequences and shape-symmetric morphic words
English
Charlier, Emilie mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
Kärki, Tomi [> >]
Rigo, Michel mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
2010
Discrete Mathematics
Elsevier Science
310
1238-1252
Yes (verified by ORBi)
International
0012-365X
Amsterdam
The Netherlands
[en] morphism ; abstract numeration system ; bidimensional pictures
[en] An infinite word is S-automatic if, for all n>=0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study its relation to the shapesymmetric infinite words introduced by Arnaud Maes. More precisely, for d>1, we show that a multidimensional infinite word x over a finite alphabet is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word.
Researchers ; Professionals
http://hdl.handle.net/2268/32179
10.1016/j.disc.2009.12.002

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