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Minkowski's Theorem
| Title: | Minkowski's Theorem |
| Author: | Manuel Eberl |
| Submission date: | 2017-07-13 |
| Abstract: |
Minkowski's theorem relates a subset of ℝn, the Lebesgue measure, and the integer lattice ℤn: It states that any convex subset of ℝn with volume greater than 2n contains at least one lattice point from ℤn\{0}, i. e. a non-zero point with integer coefficients. A related theorem which directly implies this is Blichfeldt's theorem, which states that any subset of ℝn with a volume greater than 1 contains two different points whose difference vector has integer components. The entry contains a proof of both theorems. |
| BibTeX: |
@article{Minkowskis_Theorem-AFP,
author = {Manuel Eberl},
title = {Minkowski's Theorem},
journal = {Archive of Formal Proofs},
month = jul,
year = 2017,
note = {\url{http://isa-afp.org/entries/Minkowskis_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Status: [ok] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
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