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Article

Keywords:
packing; cube
Summary:
Any collection of non-blocking four-dimensional cubes, whose total volume does not exceed 17/81, can be packed into the unit four-dimensional cube. This bound is tight for the parallel packing.
References:
[1] Januszewski, J.: Packing rectangles into the unit square. Geom. Dedicata 8 (2000), 13–18. DOI 10.1023/A:1005263703808 | MR 1772192
[2] Januszewski, J., Zielonka, Ł.: Packing a triangle by sequences of its non-blocking homothetic copies. Period. Math. Hung., accepted. MR 1694593
[3] Januszewski, J., Zielonka, Ł.: Packing of non-blocking cubes into the unit cube. Beiträge Algebra Geom., https://doi.org/10.1007/s13366-023-00710-1 DOI 10.1007/s13366-023-00710-1 | MR 4779543
[4] Januszewski, J., Zielonka, Ł.: Packing of non-blocking squares into the unit square. Colloq. Math., https://doi.org/10.4064/cm9006-12-2023 DOI 10.4064/cm9006-12-2023
[5] Januszewski, J., Zielonka, Ł.: Reserve in packing cubes into the unit cube. Bull. Pol. Acad. Sci. Math. 71 (2023), 85–95. DOI 10.4064/ba230215-21-6 | MR 4622411
[6] Meir, A., Moser, L.: On packing of squares and cubes. J. Combin. Theory 5 (1968), 126–134. DOI 10.1016/S0021-9800(68)80047-X | MR 0229142
[7] Moon, J.W., Moser, L.: Some packing and covering theorems. Colloq. Math. 17 (1967), 103–110. DOI 10.4064/cm-17-1-103-110 | MR 0215197 | Zbl 0152.39502
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