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Substitutions, abstract number systems and the space filling property

Clemens FuchsRobert Tijdeman — 2006

Annales de l’institut Fourier

In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo 1 and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.

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