Substitutions, abstract number systems and the space filling property

Fuchs, Clemens; Tijdeman, Robert

Substitutions, abstract number systems and the space filling property
[Substitutions et propriété de remplissage de l’espace]

Fuchs, Clemens ; Tijdeman, Robert

Annales de l'Institut Fourier, Tome 56 (2006), p. 2345-2389 / Harvested from Numdam

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Résumé
Abstract

Dans cet article nous étudions des mots multidimensionnels engendrés par des points fixes de substitutions, et obtenus en projetant les points entiers sur la demi-droite brisée correspondante. Nous montrons que pour une grande classe de substitutions le mot correspondant est la restriction d’une fonction linéaire modulo $1$ et qu’il est possible de décider si le mot résultant remplit l’espace. La preuve utilise des réseaux et le système de numération abstrait associé à la substitution.

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.

Publié le : 2006-01-01

MR 2290784 | Zbl pre05176572 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2243
Classification: 11A63, 68R15, 37B10, 05A05, 05B25, 52C07, 52C22, 68Q45, 11K16
Mots clés: substitutions, mot limite, hyperplan discret, réseaux, automates, systèmes de numération abstraits

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     author = {Fuchs, Clemens and Tijdeman, Robert},
     title = {Substitutions, abstract number systems and the space filling property},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {2345-2389},
     doi = {10.5802/aif.2243},
     zbl = {pre05176572},
     mrnumber = {2290784},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2006__56_7_2345_0}
}

Fuchs, Clemens; Tijdeman, Robert. Substitutions, abstract number systems and the space filling property. Annales de l'Institut Fourier, Tome 56 (2006) pp. 2345-2389. doi : 10.5802/aif.2243. http://gdmltest.u-ga.fr/item/AIF_2006__56_7_2345_0/

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