A parallelogram tile fills the plane by translation in at most two distinct ways

Blondin Massé, Alexandre; Brlek, Srecko et Labbé, Sébastien (2012). « A parallelogram tile fills the plane by translation in at most two distinct ways ». Discrete Applied Mathematics, 160(7-8), pp. 1011-1018.

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Résumé

We consider the tilings by translation of a single polyomino or tile on the square grid Z2 (Z exposant 2). It is well-known that there are two regular tilings of the plane, namely, parallelogram and hexagonal tilings. Although there exist tiles admitting an arbitrary number of distinct hexagon tilings, it has been conjectured that no polyomino admits more than two distinct parallelogram tilings. In this paper, we prove this conjecture.

Type: Article de revue scientifique
Mots-clés ou Sujets: Tilings; Polyominoes
Unité d'appartenance: Faculté des sciences > Département d'informatique
Déposé par: Alexandre Blondin Massé
Date de dépôt: 09 mai 2016 14:30
Dernière modification: 30 mai 2016 14:44
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8429

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