An octomino of high order
type: Item
instance of: scholarly article
title: An octomino of high order
zbMATH Open document ID: 0815.05024
DOI: 10.1016/0097-3165(95)90085-3
author: Karl A. Dahlke
author: S. W. Golomb
author: Herbert Taylor
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-04-04T00:00:00Z
review text: The order of an \(n\)-omino is the smallest value of \(k\) such that \(k\) copies of it can be used to tile a rectangle of area \(kn\). Previous results on tiling rectangles with polyominoes have been obtained in this journal by the first author [ibid. 51, No. 1, 125-126 and 127-128 (1989; Zbl 0715.05013 and Zbl 0715.05014)], the second author [ibid. 51, No. 1, 117-124 (1989; Zbl 0723.05041)] and \textit{D. A. Klarner} [J. Comb. Theory 7, No. 2, 107-115 (1969; Zbl 0174.041)], who found an octomino of order 24. In this paper the first author has found an octomino such that 312 copies of it tile a \(26\times 96\) rectangle. The last author has found another octomino that can tile a \(32\times \infty\) half-strip. It is not known at present whether there is a rectangle that can be tiled by this octomino.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 05B50
zbMATH DE Number: 740292
zbMATH Keywords: tiling rectangles
zbMATH Keywords: octomino
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90085-3
OpenAlex ID: W1991021282
cites work: The Y-hexomino has order 92
cites work: A heptomino of order 76
cites work: Polyominoes which tile rectangles
cites work: Packing a rectangle with congruent N-ominoes
description: scientific article; zbMATH DE number 740292