@article{Bruns2016Quant-52322,
  year={2016},
  doi={10.1007/s00454-016-9773-7},
  title={Quantum Jumps of Normal Polytopes},
  number={1},
  volume={56},
  issn={0179-5376},
  journal={Discrete & Computational Geometry},
  pages={181--215},
  author={Bruns, Winfried and Gubeladze, Joseph and Michalek, Mateusz}
}

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    <dcterms:abstract xml:lang="eng">We introduce a partial order on the set of all normal polytopes in R&lt;sup&gt;d&lt;/sup&gt;. This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in R&lt;sup&gt;d&lt;/sup&gt;, ordered by inclusion, and exhibits a remarkably rich combinatorial structure. We derive various arithmetic bounds on elementary relations in NPol(d), called quantum jumps. The existence of extremal objects in NPol(d) is a challenge of number theoretical flavor, leading to interesting classes of normal polytopes: minimal, maximal, spherical. Minimal elements in NPol(5) have played a critical role in disproving various covering conjectures for normal polytopes in the 1990s. Here we report on the first examples of maximal elements in NPol(4) and NPol(5), found by a combination of the developed theory, random generation, and extensive computer search.</dcterms:abstract>
    <dc:language>eng</dc:language>
    <dcterms:issued>2016</dcterms:issued>
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    <dcterms:title>Quantum Jumps of Normal Polytopes</dcterms:title>
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    <dc:contributor>Bruns, Winfried</dc:contributor>
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    <dc:contributor>Michalek, Mateusz</dc:contributor>
    <dc:creator>Gubeladze, Joseph</dc:creator>
    <dc:creator>Michalek, Mateusz</dc:creator>
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    <dc:contributor>Gubeladze, Joseph</dc:contributor>
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    <dc:creator>Bruns, Winfried</dc:creator>
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