Combinatorics/Geometry
The Heesch number for multiple prototiles is unbounded
[Le nombre de Heesch pour plusieurs proto-pavés est non borné]

Présenté par : the Editorial Board

Bašić, Bojan1
1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia
Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 665-669.

Dans cette note, on prouve que, pour tous entiers k⩾3 et n⩾1, il existe un proto-ensemble qui possède k proto-pavés et dont le nombre de Heesch est égal à n. Cela réfute une conjecture de Grünbaum et Shephard.

In this paper we show that, for all integers k⩾3 and n⩾1, there exists a protoset consisting of k prototiles, whose Heesch number is n. This disproves a conjecture by Grünbaum and Shephard.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.05.002
Bašić, Bojan 1

1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia 
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Bašić, Bojan. The Heesch number for multiple prototiles is unbounded. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 665-669. doi : 10.1016/j.crma.2015.05.002. http://archive.numdam.org/articles/10.1016/j.crma.2015.05.002/

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