Sails and Hilbert Bases
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 98-105
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A sail is the boundary of a Klein polyhedron. A relation between certain properties of sails is determined. In particular, a criterion is presented for the Hilbert basis of the semigroup of integer points of a cone in $\mathbb R^3$ and $\mathbb R^4$ to be contained in the sail.
@article{TM_2002_239_a5,
author = {O. N. German},
title = {Sails and {Hilbert} {Bases}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {98--105},
year = {2002},
volume = {239},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2002_239_a5/}
}
O. N. German. Sails and Hilbert Bases. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 98-105. http://geodesic.mathdoc.fr/item/TM_2002_239_a5/
[1] Lachaud G., “Sails and Klein polyhedra”, Contemp. Math., 210, 1998, 373–385 | MR | Zbl
[2] Lachaud G., Voiles et polyèdres de Klein, 1, 2, Preprints No 95–22, Lab. Math. Discr., CNRS, Marseille–Luminy, 1995
[3] Mussafir Zh.-O., “Parusa i bazisy Gilberta”, Funkts. analiz i ego pril., 34:2 (2000), 43–49 | MR
[4] Bryuno A. D., Parusnikov V. I., “Mnogogranniki Kleina dlya dvukh kubicheskikh form Davenporta”, Mat. zametki, 56:4 (1994), 9–27 | MR | Zbl
[5] White G. K., “Lattice tetrahedra”, Canad. J. Math., 16 (1964), 389–396 | MR | Zbl