A stability theorem on cube tessellations

János Pach, Peter Frankl

Abstract


It is shown that if a $d$-dimensional cube is decomposed into $n$ cubes, the side lengths
of which belong to the interval $(1 − \frac{n}{1/d 1 +1} , 1]$, then $n$ is a perfect $d$-th power and all
cubes are of the same size. This result is essentially tight.


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DOI: http://dx.doi.org/10.20382/jocg.v9i1a13

ISSN: 1920-180X