Geodesic
On some vector balancing problems
Studia Mathematica, Tome 122 (1997) no. 3, pp. 225-234

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let V be an origin-symmetric convex body in $ℝ^n$, n≥ 2, of Gaussian measure $γ_n(V)≥ 1/2$. It is proved that for every choice $u_1,...,u_n$ of vectors in the Euclidean unit ball $B_n$, there exist signs $ε_j ∈ {-1,1}$ with $ε_{1}u_{1} + ... + ε_{n}u_{n} ∈ (clogn)V$. The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.
DOI : 10.4064/sm-122-3-225-234

Apostolos A. Giannopoulos 1

1 
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Apostolos A.  Giannopoulos. On some vector balancing problems. Studia Mathematica, Tome 122 (1997) no. 3, pp. 225-234. doi: 10.4064/sm-122-3-225-234

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