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Model. Anal. Inform. Sist., 2013, Volume 20, Number 6, Pages 129–134 (Mi mais349)  

This article is cited in 1 scientific paper (total in 1 paper)

A Definition of Type Domain of a Parallelotope

V. P. Grishukhin

Central Economics and Mathematics Institute RAS, Nakhimovskii prosp., 47, Moscow, 117418, Russia

Abstract: Each convex polytope $P=P(\alpha)$ can be described by a set of linear inequalities determined by vectors $p$ and right hand sides $\alpha(p)$. For a fixed set of vectors $p$, a type domain ${\mathcal D}(P_0)$ of a polytope $P_0$ and, in particular, of a parallelotope $P_0$ is defined as a set of parameters $\alpha(p)$ such that polytopes $P(\alpha)$ have the same combinatorial type as $P_0$ for all $\alpha\in{\mathcal D}(P_0)$.
In the second part of the paper, a facet description of zonotopes and zonotopal parallelotopes are given.
The article is published in the author's wording.

Keywords: parallelotope, type domain, zonotope.

Full text: PDF file (385 kB)
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UDC: 511.6
Received: 10.10.2013
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Citation: V. P. Grishukhin, “A Definition of Type Domain of a Parallelotope”, Model. Anal. Inform. Sist., 20:6 (2013), 129–134

Citation in format AMSBIB
\Bibitem{Gri13}
\by V.~P.~Grishukhin
\paper A Definition of Type Domain of a Parallelotope
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 6
\pages 129--134
\mathnet{http://mi.mathnet.ru/mais349}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Grishukhin, “Parallelohedra defined by quadratic forms”, Proc. Steklov Inst. Math., 288 (2015), 81–93  mathnet  crossref  crossref  isi  elib
  • Моделирование и анализ информационных систем
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