Sails and Hilbert bases
Moussafir, Jacques-Olivier (2000), Sails and Hilbert bases, Functional Analysis and its Applications, 34, 2, p. 114-118. http://dx.doi.org/10.1007/BF02482424
TypeArticle accepté pour publication ou publié
Journal nameFunctional Analysis and its Applications
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Abstract (EN)A Klein polyhedron is the convex hull of the nonzero integral points of a simplicial coneC⊂ ℝn. There are relationships between these polyhedra and the Hilbert bases of monoids of integral points contained in a simplicial cone. In the two-dimensional case, the set of integral points lying on the boundary of a Klein polyhedron contains a Hilbert base of the corresponding monoid. In general, this is not the case if the dimension is greater than or equal to three (e.g., ). However, in the three-dimensional case, we give a characterization of the polyhedra that still have this property. We give an example of such a sail and show that our criterion does not hold if the dimension is four.
Subjects / KeywordsHilbert base; Klein polyhedron
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