On some vector balancing problems

Studia Mathematica

Volumn 122, Issue 3, 1997, Pages 225-234

  Giannopoulos, Apostolos A ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039270509     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm-122-3-225-234     Document Type: Article

References (15)

1. K. Ball and A. Pajor, Convex bodies with few faces, Proc. Amer. Math. Soc. 110 (1990), 225-231.
2. W. Banaszczyk, Balancing vectors and convex bodies, Studia Math. 106 (1993), 93-100.
3. _, A Beck-Fiala-type theorem for Euclidean norms, European J. Combin. 11 (1990), 497-500.
4. W. Banaszczyk and S. J. Szarek, Lattice coverings and Gaussian measures of n-dimensional convex bodies, Discrete Comput. Geom., to appear.
5. I. Bárány and V. S. Grinberg, On some combinatorial questions in finite-dimensional spaces, Linear Algebra Appl. 41 (1981), 1-9.
6. J. Beck and T. Fiala, Integer-making theorems, Discrete Appl. Math. 3 (1981), 1-8.
7. E. D. Gluskin, Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces, Math. USSR-Sb. 64 (1989), 85-96.
8. B. S. Kashin, An analogue of Menshov's "correction" theorem for discrete orthonormal systems, Mat. Zametki 46 (6) (1989), 67-74 (in Russian); English transl.: Math. Notes 46 (5-6) (1989), 934-939.
9. B. S. Kashin, An analogue of Menshov's "correction" theorem for discrete orthonormal systems, Mat. Zametki 46 (6) (1989), 67-74 (in Russian); English transl.: Math. Notes 46 (5-6) (1989), 934-939.
10. D. Kleitman, On a combinatorial conjecture of Erdos, J. Combin. Theory Ser. A 1 (1966), 209-214.
11. Z. Sidák, On multivariate normal probabilities of rectangles: their dependence on correlation, Ann. Math. Statist. 39 (1968), 1425-1434.
12. J. Spencer, Six standard deviations suffice, Trans. Amer. Math. Soc. 289 (1985), 679-706.
13. _, Balancing vectors in the max norm, Combinatorica 6 (1) (1986), 55-65.
14. _, Ten Lectures on the Probabilistic Method, SIAM, Philadelphia, Penn., 1994.
15. S. J. Szarek and E. Werner, Confidence regions for means of multivariate normal distributions and a non-symmetric correlation inequality for Gaussian measure, preprint.