Geodesic
Sails and Hilbert Bases
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 2, pp. 43-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - J. Moussafir
TI  - Sails and Hilbert Bases
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2000
SP  - 43
EP  - 49
VL  - 34
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a4/
LA  - ru
ID  - FAA_2000_34_2_a4
ER  - 
%0 Journal Article
%A J. Moussafir
%T Sails and Hilbert Bases
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2000
%P 43-49
%V 34
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2000_34_2_a4/
%G ru
%F 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/

[1] Arnold V. I., “A-graded algebras and continued fractions”, Commun. Pure Appl. Math., 42 (1989), 993–1000 | DOI | MR | Zbl

[2] Korkina E., “Classification of A-graded algebas with $3$ generators”, Indag. Math. (NS), 3(1) (1992), 27–40 | DOI | MR | Zbl

[3] Korkina E. I., “Dvumernye nepreryvnye drobi. Prosteishie primery”, Trudy MIAN, 209, 1995, 143–166 | MR | Zbl

[4] Lachaud G., Voiles et Polyédres de Klein, Prétirage 95–22. Laboratoire de Mathématiques Discrétes, CNRS, 1995