Packing of non-blocking cubes into the unit cube. (English) Zbl 07909690
Summary: Any collection of non-blocking cubes, whose total volume does not exceed 1/3, can be packed into the unit cube.
MSC:
| 52C17 | Packing and covering in \(n\) dimensions (aspects of discrete geometry) |
References:
| [1] | Januszewski, J., Zielonka, Ł.: Packing a triangle by sequences of its non-blocking homothetic copies. Period. Math. Hung. accepted (2023a) |
| [2] | Januszewski, J., Zielonka, Ł.: Packing of non-blocking squares into the unit square, submitted (2023b) |
| [3] | Januszewski, J.; Zielonka, Ł., Packing batches of items into a single bin, Inform. Process. Lett., 174, 106196, 2022 · Zbl 1533.68415 · doi:10.1016/j.ipl.2021.106196 |
| [4] | Januszewski, J.; Zielonka, Ł., Packing batches of cubes into a single bin, Inform. Process. Lett., 180, 106337, 2023 · Zbl 07647060 · doi:10.1016/j.ipl.2022.106337 |
| [5] | Meir, A.; Moser, L., On packing of squares and cubes, J. Combin. Theory, 5, 126-134, 1968 · Zbl 0165.25202 · doi:10.1016/S0021-9800(68)80047-X |
| [6] | Moon, JW; Moser, L., Some packing and covering theorems, Colloq. Math., 17, 103-110, 1967 · Zbl 0152.39502 · doi:10.4064/cm-17-1-103-110 |
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