Klamer systems and tiling boxes with polyominoes

    Authors

    M. Reid

    Comments

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    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

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