# On some vector balancing problems

Studia Mathematica (1997)

- Volume: 122, Issue: 3, page 225-234
- ISSN: 0039-3223

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topGiannopoulos, Apostolos. "On some vector balancing problems." Studia Mathematica 122.3 (1997): 225-234. <http://eudml.org/doc/216373>.

@article{Giannopoulos1997,

abstract = {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.},

author = {Giannopoulos, Apostolos},

journal = {Studia Mathematica},

keywords = {balancing problem},

language = {eng},

number = {3},

pages = {225-234},

title = {On some vector balancing problems},

url = {http://eudml.org/doc/216373},

volume = {122},

year = {1997},

}

TY - JOUR

AU - Giannopoulos, Apostolos

TI - On some vector balancing problems

JO - Studia Mathematica

PY - 1997

VL - 122

IS - 3

SP - 225

EP - 234

AB - 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.

LA - eng

KW - balancing problem

UR - http://eudml.org/doc/216373

ER -

## References

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