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A sharp combinatorial version of Vaaler's theorem
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Ball, Keith M. and Prodromou, M. (2009) A sharp combinatorial version of Vaaler's theorem. Bulletin of the London Mathematical Society, Vol.41 (No.5). pp. 853-858. doi:10.1112/blms/bdp062 ISSN 0024-6093 .
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Official URL: http://dx.doi.org/10.1112/blms/bdp062
Abstract
In 1979 Vaaler proved that every d-dimensional central section of the cube [−1, 1]n has volume at least 2d. We prove the following sharp combinatorial analogue. Let K be a d-dimensional subspace of ℝn. Then, there exists a probability measure P on the section [−1, 1]n ∩ K such that the quadratic form
dominates the identity on K (in the sense that the difference is positive semi-definite).
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Bulletin of the London Mathematical Society | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0024-6093 | ||||
| Official Date: | October 2009 | ||||
| Dates: |
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| Volume: | Vol.41 | ||||
| Number: | No.5 | ||||
| Page Range: | pp. 853-858 | ||||
| DOI: | 10.1112/blms/bdp062 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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