Comptes Rendus
no. 8
Combinatorics/Geometry
The Heesch number for multiple prototiles is unbounded
the Editorial Board
Bojan Bašić1
1Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia
Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 665-669

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.05.002

Bojan Bašić  1

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