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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 2, Pages 43–49 (Mi faa294)  

This article is cited in 11 scientific papers (total in 11 papers)

Sails and Hilbert Bases

J.-O. Moussafir

Université Paris-Dauphine

Abstract: 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.

DOI: https://doi.org/10.4213/faa294

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English version:
Functional Analysis and Its Applications, 2000, 34:2, 114–118

Bibliographic databases:

UDC: 512.7+514.17
Received: 16.09.1998

Citation: J. Moussafir, “Sails and Hilbert Bases”, Funktsional. Anal. i Prilozhen., 34:2 (2000), 43–49; Funct. Anal. Appl., 34:2 (2000), 114–118

Citation in format AMSBIB
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\issue 2
\pages 43--49
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\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 2
\pages 114--118
\crossref{https://doi.org/10.1007/BF02482424}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. N. German, “Sails and Hilbert Bases”, Proc. Steklov Inst. Math., 239 (2002), 88–95  mathnet  mathscinet  zmath
    2. O. N. Karpenkov, “On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities”, Funct. Anal. Appl., 38:2 (2004), 102–110  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. O. N. German, “Sails and norm minima of lattices”, Sb. Math., 196:3 (2005), 337–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. O. N. Karpenkov, “On an Invariant Möbius Measure and the Gauss–Kuzmin Face Distribution”, Proc. Steklov Inst. Math., 258 (2007), 74–86  mathnet  crossref  mathscinet  zmath  elib  elib
    5. Karpenkov, ON, “Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions”, Monatshefte fur Mathematik, 152:3 (2007), 217  crossref  mathscinet  zmath  isi  scopus
    6. Karpenkov, ON, “CONSTRUCTING MULTIDIMENSIONAL PERIODIC CONTINUED FRACTIONS IN THE SENSE OF Klein”, Mathematics of Computation, 78:267 (2009), 1687  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. I. A. Makarov, “Interior Klein Polyhedra”, Math. Notes, 95:6 (2014), 795–805  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. A. Illarionov, “Some properties of three-dimensional Klein polyhedra”, Sb. Math., 206:4 (2015), 510–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Susse T., “Stable Commutator Length in Amalgamated Free Products”, J. Topol. Anal., 7:4 (2015), 693–717  crossref  mathscinet  isi  scopus
    10. S. I. Veselov, “O tselykh tochkakh poliedrov dvukh tipov”, Zhurnal SVMO, 19:3 (2017), 24–30  mathnet  crossref  elib
    11. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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