Multidimensional generalized automatic sequences and shape-symmetric morphic words

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 shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d 1, we show that a multidimensional infinite word x: Nd over a finite alphabet omatic 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.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Emilie Charlier, Tomi Kärki, Michel Rigo
• Keywords: DM 2010, Infinite Word, Multidimensional Infinite Word, Shape-symmetric Infinite Word