The Helly dimension of the L1-sum of convex sets
It is well known that the Helly dimension of the direct sum of convex sets is the maximum of the Helly dimension of the summands. In this paper we shall investigate the Helly dimension of the Li-sum of two centrally symmetric compact convex sets. In case of the Lj-sum, the Helly dimension is not det...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2010
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| Sorozat: | Acta scientiarum mathematicarum
76 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16369 |
| Tartalmi kivonat: | It is well known that the Helly dimension of the direct sum of convex sets is the maximum of the Helly dimension of the summands. In this paper we shall investigate the Helly dimension of the Li-sum of two centrally symmetric compact convex sets. In case of the Lj-sum, the Helly dimension is not determined by the Helly dimension of the summands. Our main result is to give sharp bounds for the Helly dimension of the Li-sum depending on the Helly dimension of the summands. |
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| Terjedelem/Fizikai jellemzők: | 643-657 |
| ISSN: | 0001-6969 |