Maximal integral simplices with no interior integer points

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dc.creatorAndersen, Kent
dc.creatorWagner, Christian
dc.creatorWeismantel, Robert
dc.date2009-04-14
dc.date2009-05-19
dc.date.accessioned2026-07-07T13:15:50Z
dc.date.available2026-07-07T13:15:50Z
dc.descriptionIn this paper, we consider integral maximal lattice-free simplices. Such simplices have integer vertices and contain integer points in the relative interior of each of their facets, but no integer point is allowed in the full interior. In dimension three, we show that any integral maximal lattice-free simplex is equivalent to one of seven simplices up to unimodular transformation. For higher dimensions, we demonstrate that the set of integral maximal lattice-free simplices with vertices lying on the coordinate axes is finite. This gives rise to a conjecture that the total number of integral maximal lattice-free simplices is finite for any dimension.
dc.identifierhttps://arxiv.org/abs/0904.2108
dc.identifierhttp://arxiv.org/abs/0904.2108
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230596
dc.subjectOptimization and Control
dc.subjectCombinatorics
dc.titleMaximal integral simplices with no interior integer points
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