𝔖 Bobbio Scriptorium
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Tiling a Rectangle with the Fewest Squares

✍ Scribed by Richard Kenyon

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
594 KB
Volume
76
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

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 qΓ‚p+C log p squares of integer size, for some universal constant C.

πŸ“œ SIMILAR VOLUMES

A Note on Tiling with Integer-Sided Rect
A Note on Tiling with Integer-Sided Rectangles
✍ Richard Kenyon πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 350 KB

We show how to determine if a given rectilinear polygon can be tiled with rectangles, each having an integer side.

Tiling a Square with Eight Congruent Pol
Tiling a Square with Eight Congruent Polyominoes
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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

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