On the asymmetry constant of a body with few vertices

E. D. Gluskin; A. E. Litvak

doi:10.1023/A:1014994419758

On the asymmetry constant of a body with few vertices

E. D. Gluskin^*, A. E. Litvak

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this note, we show that a nondegenerated polytope in ℝⁿ with n + k, 1 ≤ k ≤ n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes.

Original language	English
Pages (from-to)	45-48
Number of pages	4
Journal	Geometriae Dedicata
Volume	90
Issue number	1
DOIs	https://doi.org/10.1023/A:1014994419758
State	Published - 2002

Keywords

Affine transformation
Asymmetry constant
Banach-Mazur distance
Convex bodies
Polytopes

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title = "On the asymmetry constant of a body with few vertices",

abstract = "In this note, we show that a nondegenerated polytope in ℝn with n + k, 1 ≤ k ≤ n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes.",

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AU - Gluskin, E. D.

AU - Litvak, A. E.

PY - 2002

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AB - In this note, we show that a nondegenerated polytope in ℝn with n + k, 1 ≤ k ≤ n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes.

KW - Affine transformation

KW - Asymmetry constant

KW - Banach-Mazur distance

KW - Convex bodies

KW - Polytopes

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JO - Geometriae Dedicata

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On the asymmetry constant of a body with few vertices

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