Colorful vector balancing
We extend classical estimates for the vector balancing constant of equipped with the Euclidean and the maximum norms proved in the 1980s by showing that for and , given vector families with , one may select vectors with for , and for . These bounds are sharp and asymptotically sharp, respectively, f...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | MATHEMATIKA
70 No. 4 |
| Tárgyszavak: | |
| doi: | 10.1112/mtk.12274 |
| mtmt: | 35186951 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37306 |
| Tartalmi kivonat: | We extend classical estimates for the vector balancing constant of equipped with the Euclidean and the maximum norms proved in the 1980s by showing that for and , given vector families with , one may select vectors with for , and for . These bounds are sharp and asymptotically sharp, respectively, for . The proofs combine linear algebraic and probabilistic methods with a Gaussian random walk argument. |
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| Terjedelem/Fizikai jellemzők: | 24 |
| ISSN: | 0025-5793 |