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arXiv · 0907.0615

Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words

Emilie Charlier·Tomi Karki·Michel Rigo
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Abstract

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 considered numeration system S. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d>=2, we state that a multidimensional infinite word x : N^d \to Σover a finite alphabet Σis 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.

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Emilie Charlier, Tomi Karki, Michel Rigo. 2009-07-03. Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words. https://arxiv.org/abs/0907.0615

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