Dynamical Systems
Combinatorics and topology of the Robinson tiling
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 627-631.

We study the space of all tilings which can be obtained using the Robinson tiles (this is a two-dimensional subshift of finite type). We prove that it has a unique minimal subshift, and describe it by means of a substitution. This description allows to compute its cohomology groups, and prove that it is a model set. This article has an annex which was transmitted to the Académie des Sciences.

Nous étudions lʼespace de tous les pavages qui peuvent sʼobtenir à partir des tuiles de Robinson (il sʼagit dʼun sous-décalage de type fini). Cet espace contient un unique sous-espace minimal, que nous décrivons par le biais dʼune substitution. En conséquence, il est possible de calculer les groupes de cohomologie associés, et de montrer quʼil sʼagit dʼun pavage de coupe et projection. Cet article a une annexe qui a été transmise à lʼAcadémie des Sciences.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.06.007
Gähler, Franz 1; Julien, Antoine 2; Savinien, Jean 3

1 Faculty of Mathematics, University of Bielefeld, Universitätsstraße 25, 33615 Bielefeld, Germany
2 Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, V8P 5C2 Victoria, BC, Canada
3 Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz cedex 1, France
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Gähler, Franz; Julien, Antoine; Savinien, Jean. Combinatorics and topology of the Robinson tiling. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 627-631. doi : 10.1016/j.crma.2012.06.007. http://www.numdam.org/articles/10.1016/j.crma.2012.06.007/

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