1. CUBE PACKINGS IN EUCLIDEAN SPACES
- Author
-
Han Yu
- Subjects
General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,05B30, 28A78, 52C17 ,0102 computer and information sciences ,01 natural sciences ,Combinatorics ,Packing problems ,Mathematics - Classical Analysis and ODEs ,010201 computation theory & mathematics ,Euclidean geometry ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,Cube ,Mathematics - 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., 9 pages. arXiv admin note: text overlap with arXiv:1711.06533
- Published
- 2021