The minimum sizes of maximal systems of brick islands
For integers mi,... , m^ > 0 and a cuboid M = [0, mi] x • • • x [0, m j C Rd , a set H of closed bricks in M is a system of brick islands if, for each pair of bricks in H, one contains the other or they are disjoint. Such a system is maximal if it cannot be extended to a larger system of brick is...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2012
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| Sorozat: | Acta scientiarum mathematicarum
78 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16439 |
| Tartalmi kivonat: | For integers mi,... , m^ > 0 and a cuboid M = [0, mi] x • • • x [0, m j C Rd , a set H of closed bricks in M is a system of brick islands if, for each pair of bricks in H, one contains the other or they are disjoint. Such a system is maximal if it cannot be extended to a larger system of brick islands. We show that the minimum size of a maximal system of brick islands in M is m i ~ (d — 1)- Also, a system of cubic islands is a system of brick islands for which all the bricks are cubes. We show that the minimum size of a maximal system of cubic islands in a cube C = [m]cl is m. |
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| Terjedelem/Fizikai jellemzők: | 375-387 |
| ISSN: | 0001-6969 |