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Dissectingd-Cubes into Smallerd-Cubes

✍ Scribed by Matthew Hudelson

Book ID
102583151
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
313 KB
Volume
81
Category
Article
ISSN
0097-3165

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✦ Synopsis

In this paper, we explore the following question: Given integers d and k, is it possible to subdivide a d-dimensional cube into k smaller d-dimensional cubes? In particular, we investigate bounds on the integer c(d) which is the smallest integer for which it is possible to subdivide the d-cube into any number k c(d ) smaller d-cubes. We derive specific bounds for d 5, and furthermore, we investigate, for given k, the asymptotic behavior of c(d ) for those d such that gcd(2 d &1,

Finally, we derive the general asymptotic bound c(d )=O((2d) d&1 ) which improves the currently known bound of c(d )=O((2d) d ).

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