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Cube packings in Euclidean spaces
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abstract
In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper.
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Cited by 1 Pith paper
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The Endpoint Cardinality of Discrete Cube Skeleta
For each fixed 0≤k<n, the minimum lattice set containing a filled k-skeleton about every one of N centers is Θ(N^{1-(n-k)/(2n^2)}), closing the endpoint lower bound.
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