| Title:
|
Packing of non-blocking four-dimensional cubes into the unit cube (English) |
| Author:
|
Januszewski, Janusz |
| Author:
|
Zielonka, Łukasz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
153-162 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
packing |
| Keyword:
|
cube |
| MSC:
|
52C17 |
| idZBL:
|
Zbl 07893346 |
| idMR:
|
MR4805418 |
| DOI:
|
10.5817/AM2024-3-153 |
| . |
| Date available:
|
2024-08-02T08:35:00Z |
| Last updated:
|
2025-01-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152523 |
| . |
| Reference:
|
[1] Januszewski, J.: Packing rectangles into the unit square.Geom. Dedicata 8 (2000), 13–18. MR 1772192, 10.1023/A:1005263703808 |
| Reference:
|
[2] Januszewski, J., Zielonka, Ł.: Packing a triangle by sequences of its non-blocking homothetic copies.Period. Math. Hung., accepted. MR 1694593 |
| Reference:
|
[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. MR 4779543, 10.1007/s13366-023-00710-1 |
| Reference:
|
[4] Januszewski, J., Zielonka, Ł.: Packing of non-blocking squares into the unit square.Colloq. Math., https://doi.org/10.4064/cm9006-12-2023. 10.4064/cm9006-12-2023 |
| Reference:
|
[5] Januszewski, J., Zielonka, Ł.: Reserve in packing cubes into the unit cube.Bull. Pol. Acad. Sci. Math. 71 (2023), 85–95. MR 4622411, 10.4064/ba230215-21-6 |
| Reference:
|
[6] Meir, A., Moser, L.: On packing of squares and cubes.J. Combin. Theory 5 (1968), 126–134. MR 0229142, 10.1016/S0021-9800(68)80047-X |
| Reference:
|
[7] Moon, J.W., Moser, L.: Some packing and covering theorems.Colloq. Math. 17 (1967), 103–110. Zbl 0152.39502, MR 0215197, 10.4064/cm-17-1-103-110 |
| . |
