Undecidable tiling problems in the hyperbolic plane
type: Item
instance of: scholarly article
title: Undecidable tiling problems in the hyperbolic plane
zbMATH Open document ID: 0354.50006
DOI: 10.1007/BF01403163
author: Raphael M. Robinson
published in: Inventiones Mathematicae
publication date: 1978-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/142530
review text: In his earlier paper [Invent. Math. 12, 177--209 (1970; Zbl 0197.46801)] the author proposed the problem of extending to the hyperbolic plane the undecidability and nonperiodicity results known for tilings of the Euclidean plane. In the present paper he succeeds in extending the undecidability results for the simplest case, that is, the origin-constrained case. He also finds a set of 49 polygons for which the completion problem is undecidable. The other problems remain open.
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 03D35
zbMATH DE Number: 3551487
MaRDI profile type: Publication
cites work: The undecidability of the domino problem
cites work: Nonrecursive tilings of the plane. I
cites work: Nonrecursive tilings of the plane. II
OpenAlex ID: W2013120724
description: scientific article; zbMATH DE number 3551487