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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.
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
Linking options:
https://www.mathnet.ru/eng/mzm9340https://doi.org/10.4213/mzm9340 https://www.mathnet.ru/eng/mzm/v95/i6/p854
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