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Classifications and volume bounds of lattice polytopes
Stockholm University, Faculty of Science, Department of Mathematics.
2017 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional lattice polytopes with two lattice points in their strict interior. Up to unimodular equivalence thereare 22,673,449 such polytopes. This classification allows us to verify, for this case only, the sharp conjectural upper bound for the volume of a lattice polytope with interior points, and provides strong evidence for more general new inequalities on the coefficients of the h^*-polynomial in dimension three.

Place, publisher, year, edition, pages
Stockholm University, 2017.
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:su:diva-139823OAI: oai:DiVA.org:su-139823DiVA, id: diva2:1074613
Presentation
2017-03-08, 15:15
Opponent
Supervisors
Available from: 2017-03-01 Created: 2017-02-15 Last updated: 2017-03-01Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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  • de-DE
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  • en-US
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  • nn-NB
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  • Other locale
More languages
Output format
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