Non-repetitive tilings
type: Item
instance of: scholarly article
title: Non-repetitive tilings
zbMATH Open document ID: 1004.05020
author: James D. Currie
author: Jamie Simpson
published in: The Electronic Journal of Combinatorics
publication date: 2002-07-25T00:00:00Z
full work available at URL: https://eudml.org/doc/122338
full work available at URL: v9i1r28.html
review text: Summary: In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope \(+1\) or \(-1\) contain no repetitions. As part of the construction we introduce a new type of word, one that is non-repetitive up to \(\text{mod }k\), which is of interest in itself. We also indicate how our results might be extended to higher dimensions.
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 11B99
zbMATH DE Number: 1770058
zbMATH Keywords: rectangular tiling of the plane
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1770058