On some vector balancing problems

• Autorzy: Giannopoulos Apostolos A.
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 52C07: Lattices and convex bodies in n dimensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 3
• Strony: 225-234

Daty

wydano

1997

otrzymano

1995-10-25

poprawiono

1996-06-19

poprawiono

1996-09-18

Twórcy

autor

Giannopoulos Apostolos A.

• Department of Mathematics, University of Crete Iraklion, Crete, Greece

Bibliografia

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