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Polyominoes which tile rectangles

โœ Scribed by Solomon W. Golomb


Book ID
107885120
Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
344 KB
Volume
51
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES


Tiling Rectangles and Half Strips with C
โœ Michael Reid ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 322 KB

In the second edition of Golomb's classic ``Polyominoes'' [9], several infinite families of rectifiable polyominoes are given, but only nine sporadic examples are known. Curiously, two of these sporadic examples are related by a 2\_1 affine transformation (Fig. 1). This led us to consider the image

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Golomb has covered the main previous results of tiling a rectangle with congruent polyominoes in the revised edition of ``Polyominoes' ' (1994). This article attempts to summarise recent discoveries of many new examples of polyominoes which pack rectangles.

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We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes and show that the criterion detects some cases that are not detecta