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 qรp+C log p squares of integer size, for some universal constant C.
A Note on Tiling with Integer-Sided Rectangles
โ Scribed by Richard Kenyon
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 350 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
โฆ Synopsis
We show how to determine if a given rectilinear polygon can be tiled with rectangles, each having an integer side.
๐ SIMILAR VOLUMES
A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. We consider the problem of finding necessary and sufficient conditions for a finite set to tile the integers. For sets of prime power ลฝ . size, it was solved by D. Newman 1977, J. Numbe
The enumeration problem of Latin rectangles is formulated in terms of permanents, and two 'hard' inequalities of permanents are applied in a squeezing manner, both giving and suggesting asymptotic formulas.