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CUBE PACKINGS IN EUCLIDEAN SPACES
Author(s) -
Yu Han
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12074
Subject(s) - cube (algebra) , mathematics , dimension (graph theory) , euclidean geometry , combinatorics , euclidean space , packing dimension , euclidean distance , unit cube , geometry , minkowski–bouligand dimension , mathematical analysis , fractal dimension , fractal
In this paper, we study some cube packing problems. In particular, we are interested in compact subsets ofR n , n ⩾ 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.