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Tiling the unit square with squares and rectangles

โœ Scribed by Jim Owings


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
282 KB
Volume
40
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES


Tiling a Rectangle with the Fewest Squar
โœ Richard Kenyon ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 594 KB

We show that a square-tiling of a p\_q rectangle, where p and q are relatively prime integers, has at least log 2 p squares. If q>p we construct a square-tiling with less than qร‚p+C log p squares of integer size, for some universal constant C.

Signed Tilings with Squares
โœ Kevin Keating; Jonathan King ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 232 KB

Let T be a bounded region in the Cartesian plane built from finitely many rectangles of the form [a 1 , a 2 )\_[b 1 , b 2 ), with a 1 <a 2 and b 1 <b 2 . We give a necessary and sufficient condition for T to be tilable with finitely many positive and negative squares.

Tiling a Square with Eight Congruent Pol
โœ Michael Reid ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 76 KB

The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangula