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Matematicheskie Zametki, 2014, Volume 95, Issue 6, Pages 854–866
DOI: https://doi.org/10.4213/mzm9340 (Mi mzm9340) 		 
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
Full-text PDF (545 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm9340
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.
Received: 01.11.2012
Revised: 03.10.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 6, Pages 795–805
DOI: https://doi.org/10.1134/S0001434614050241
Bibliographic databases:
Document Type: Article
UDC: 511.9
Language: Russian
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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    • This publication is cited in the following 2 articles:
    1. A. A. Illarionov, “The statistical properties of 3D Klein polyhedra”, Sb. Math., 211:5 (2020), 689–708  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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