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Mat. Zametki, 2014, Volume 95, Issue 6, Pages 854–866 (Mi mz9340)  

This article is cited in 2 scientific papers (total in 2 papers)

Interior Klein Polyhedra

I. A. Makarovab

a M. V. Lomonosov Moscow State University
b National Research University "Higher School of Economics", Moscow

Abstract: The convex hull of all integer points of a noncompact polyhedron is closed and is a generalized polyhedron only under certain conditions. It is proved that if only the integer points in the interior of the polyhedron are taken, then most of the conditions can be dropped. Moreover, the object thus obtained has properties resembling those of a Klein polyhedron, and it is a Klein polyhedron in the case of an irrational simplicial cone.

Keywords: continued fraction, Klein polyhedron, interior Klein polyhedron, simplicial cone.

DOI: https://doi.org/10.4213/mzm9340

Full text: PDF file (545 kB)
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English version:
Mathematical Notes, 2014, 95:6, 795–805

Bibliographic databases:

UDC: 511.9
Received: 01.11.2012
Revised: 03.10.2013

Citation: I. A. Makarov, “Interior Klein Polyhedra”, Mat. Zametki, 95:6 (2014), 854–866; Math. Notes, 95:6 (2014), 795–805

Citation in format AMSBIB
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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. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
    2. A. A. Illarionov, “The statistical properties of 3D Klein polyhedra”, Sb. Math., 211:5 (2020), 689–708  mathnet  crossref  crossref  isi
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