Structural aspects of tilings - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2008

Structural aspects of tilings

Résumé

In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in two different contexts: the first one is combinatorial and the other topological. These two approaches have independent merits and, once combined, provide somehow surprising results. The particular case where the set of produced tilings is countable is deeply investigated while we prove that the uncountable case may have a completely different structure. We introduce a pattern preorder and also make use of Cantor-Bendixson rank. Our first main result is that a tile-set that produces only periodic tilings produces only a finite number of them. Our second main result exhibits a tiling with exactly one vector of periodicity in the countable case.
Fichier principal
Vignette du fichier
Ballier.pdf (220.15 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00145800 , version 1 (11-05-2007)
hal-00145800 , version 2 (14-02-2008)

Identifiants

Citer

Alexis Ballier, Bruno Durand, Emmanuel Jeandel. Structural aspects of tilings. STACS 2008, Feb 2008, Bordeaux, France. pp.61-72. ⟨hal-00145800v2⟩
151 Consultations
105 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More