Sails and Hilbert Bases
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 43-49
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A Klein polyhedron is the convex hull of the nonzero integral points of a simplicial cone $C\subset\mathbb{R}^n$. 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. 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.
@article{FAA_2000_34_2_a4,
author = {J. Moussafir},
title = {Sails and {Hilbert} {Bases}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {43--49},
publisher = {mathdoc},
volume = {34},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a4/}
}
J. Moussafir. Sails and Hilbert Bases. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 43-49. http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a4/