Tiling with notched cubes
type: Item
instance of: scholarly article
title: Tiling with notched cubes
zbMATH Open document ID: 0946.05023
DOI: 10.1016/S0012-365X(99)00310-6
author: Yanyan Li
published in: Discrete Mathematics
publication date: 2000-10-18T00:00:00Z
review text: It was known [see \textit{S. W. Golomb}, J. Comb. Theory 1, 280-296 (1966; Zbl 0143.44202)] that any polyomino which tiles a rectangle also tiles a larger copy of itself. It is not natural to expect the converse to be true but there has been no counterexample. In the paper such counterexamples are found for dimensions \(d>2.\) The author exhibits a polycube (a ``notched cube'') that tiles a large copy of itself, but does not tile any box. He obtains related results about tiling with this figure as well.
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 52C22
zbMATH DE Number: 1423748
zbMATH Keywords: polyomino
zbMATH Keywords: tiling
reviewed by: Nikolai L. Manev
MaRDI profile type: Publication
Wikidata QID: Q126571544
full work available at URL: s0012-365x(99)00310-6
OpenAlex ID: W1976243579
description: scientific article; zbMATH DE number 1423748