The Heesch number for multiple prototiles is unbounded

Bojan Bašić

doi:10.1016/j.crma.2015.05.002

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

Bojan Bašić ¹

¹ Department 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.

Résumé
Abstract

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 : 2014-10-15
Accepté le : 2015-05-19
Publié le : 2015-06-17

DOI : 10.1016/j.crma.2015.05.002

Affiliations des auteurs :

Bojan Bašić ¹

¹ Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia

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     title = {The {Heesch} number for multiple prototiles is unbounded},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.05.002/

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