Sciweavers

Share
COMBINATORICS
2004

When Can You Tile a Box With Translates of Two Given Rectangular Bricks?

8 years 5 months ago
When Can You Tile a Box With Translates of Two Given Rectangular Bricks?
When can a d-dimensional rectangular box R be tiled by translates of two given d-dimensional rectangular bricks B1 and B2? We prove that R can be tiled by translates of B1 and B2 if and only if R can be partitioned by a hyperplane into two sub-boxes R1 and R2 such that Ri can be tiled by translates of the brick Bi alone (i = 1, 2). Thus an obvious sufficient condition for a tiling is also a necessary condition. (However, there may be tilings that do not give rise to a bipartition of R.) There is an equivalent formulation in terms of the (not necessarily integer) edge lengths of R, B1, and B2. Let R be of size z1
Richard J. Bower, T. S. Michael
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMBINATORICS
Authors Richard J. Bower, T. S. Michael
Comments (0)
books