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Proof of a conjecure of Barany, Katchalski and Pach Naszodi, Marton
Description
B\'ar\'any, Katchalski and Pach proved the following quantitative form of
Helly's theorem: If the intersection of a family of convex sets in
$\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at
most $2d$ members is of volume at most some constant $v(d)$. They gave the
bound $v(d)\leq d^{2d2}$, and conjectured that $v(d)\leq d^{cd}$.
We confirmed it. We discuss the proof and further results.
Item Metadata
| Title |
Proof of a conjecure of Barany, Katchalski and Pach
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-10-25T09:55
|
| Description |
B\'ar\'any, Katchalski and Pach proved the following quantitative form of
Helly's theorem: If the intersection of a family of convex sets in
$\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at
most $2d$ members is of volume at most some constant $v(d)$. They gave the
bound $v(d)\leq d^{2d2}$, and conjectured that $v(d)\leq d^{cd}$.
We confirmed it. We discuss the proof and further results.
|
| Extent |
45 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Eötvös University
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| Series | |
| Date Available |
2017-06-06
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0348138
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International