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Comptes Rendus Mathématique
Volume 353, n° 8
pages 665-669 (août 2015)
Doi : 10.1016/j.crma.2015.05.002
Received : 15 October 2014 ;  accepted : 19 May 2015
The Heesch number for multiple prototiles is unbounded
Le nombre de Heesch pour plusieurs proto-pavés est non borné
 

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

Abstract

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

The full text of this article is available in PDF format.
Résumé

Dans cette note, on prouve que, pour tous entiers   et  , 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.

The full text of this article is available in PDF format.


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