Title

Klamer systems and tiling boxes with polyominoes

Authors

Authors

M. Reid

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Comb. Theory Ser. A

Keywords

tiling; polyomino; rectangle; prime rectangle; CONGRUENT POLYOMINOES; RECTANGLES; TILE; Mathematics

Abstract

Let T be a protoset of d-dimensional polyominoes. Which boxes (rectangular parallelepipeds) can be tiled by T? A nice result of Klarner and Gobel asserts that the answer to this question can always be given in a particularly simple form, namely, by giving a finite list of "prime" boxes. All other boxes that can be tiled can be deduced from these prime boxes. We give a new, simpler proof of this fundamental result. We also show that there is no upper bound to the number of prime boxes, even when restricting attention to singleton protosets. In the last section, we determine the set of prime rectangles for several small polyominoes. (c) 2004 Elsevier Inc. All rights reserved.

Journal Title

Journal of Combinatorial Theory Series A

Volume

111

Issue/Number

1

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

89

Last Page

105

WOS Identifier

WOS:000230048600006

ISSN

0097-3165

Share

COinS