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.
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.
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@article{CRMATH_2012__350_11-12_627_0, author = {G\"ahler, Franz and Julien, Antoine and Savinien, Jean}, title = {Combinatorics and topology of the {Robinson} tiling}, journal = {Comptes Rendus. Math\'ematique}, pages = {627--631}, publisher = {Elsevier}, volume = {350}, number = {11-12}, year = {2012}, doi = {10.1016/j.crma.2012.06.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2012.06.007/} }
TY - JOUR AU - Gähler, Franz AU - Julien, Antoine AU - Savinien, Jean TI - Combinatorics and topology of the Robinson tiling JO - Comptes Rendus. Mathématique PY - 2012 SP - 627 EP - 631 VL - 350 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.06.007/ DO - 10.1016/j.crma.2012.06.007 LA - en ID - CRMATH_2012__350_11-12_627_0 ER -
%0 Journal Article %A Gähler, Franz %A Julien, Antoine %A Savinien, Jean %T Combinatorics and topology of the Robinson tiling %J Comptes Rendus. Mathématique %D 2012 %P 627-631 %V 350 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.06.007/ %R 10.1016/j.crma.2012.06.007 %G en %F CRMATH_2012__350_11-12_627_0
Gähler, Franz; Julien, Antoine; Savinien, Jean. Combinatorics and topology of the Robinson tiling. Comptes Rendus. Mathématique, Tome 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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