Pairs of tiles which admit finitely or countably infinitely many tilings
type: Item
instance of: scholarly article
title: Pairs of tiles which admit finitely or countably infinitely many tilings
zbMATH Open document ID: 0586.52009
DOI: 10.1007/BF00164394
published in: Geometriae Dedicata
publication date: 1986-01-01T00:00:00Z
review text: Let \({\mathcal P}\) be a set of prototiles, i.e. a finite set of tiles. If a tiling exists such that every tile of it is congruent to a prototile from \({\mathcal P}\), we say that \({\mathcal P}\) admits a tiling. It is proved that for every \(k\geq 2\) and \(r\geq 1\) there exists a set of k prototiles which admits exactly r distinct tilings. The author works with the case of 2 prototiles and later easy derives the solution for every \(k>2\). It is also shown that there exist pairs of prototiles which admit countable infinity of different tilings.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 3940139
zbMATH Keywords: prototiles
zbMATH Keywords: tiling
author: Peter H. Schmitt
reviewed by: Marek Lassak
MaRDI profile type: Publication
cites work: Polymorphic Polyominoes
full work available at URL: https://doi.org/10.1007/bf00164394
OpenAlex ID: W2008450305
description: scientific article; zbMATH DE number 3940139