Abstract
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., [2]). 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.
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CEREMADE, University Paris 9. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 43–49, April–June, 2000.
Translated by J.-O. Moussafir
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Moussafir, J.O. Sails and Hilbert bases. Funct Anal Its Appl 34, 114–118 (2000). https://doi.org/10.1007/BF02482424
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DOI: https://doi.org/10.1007/BF02482424