File:Blichfeldt-Minkowski comparison.svg
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DescriptionBlichfeldt-Minkowski comparison.svg |
English: An example showing the increased power of Blichfeldt's theorem over Minkowski's theorem for finding lattice points in non-convex sets. The (closed) yellow set on the left has area 1, so by Blichfeldt's theorem it can be translated to cover two points of any lattice whose fundamental region has volume 1, such as the red lattice. It follows that the blue set on the left, the set of differences of pairs of points in , when centered on a lattice point, also contains at least one other lattice point as well as the center. In contrast, the blue rectangle on the right, the largest convex subset of , has too small an area for Minkowski's theorem to guarantee that it contains another lattice point, and the smaller yellow rectangle within it is too small to apply Blichfeldt's theorem. |
Date | |
Source | Own work |
Author | David Eppstein |
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
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http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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current | 07:23, 22 December 2020 | 652 × 396 (2 KB) | David Eppstein (talk | contribs) | Uploaded own work with UploadWizard |
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Width | 651.5 |
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Height | 396 |