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Probl. Peredachi Inf., 2012, Volume 48, Issue 2, Pages 113–120 (Mi ppi2079)  

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

Large Systems

Geometric relationship between parallel hyperplanes, quadrics, and vertices of a hypercube

K. Yu. Gorbunov, A. V. Seliverstov, V. A. Lyubetsky

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: In a space of dimension $30$ we find a pair of parallel hyperplanes, uniquely determined by vertices of a unit cube lying on them, such that strictly between the hyperplanes there are no vertices of the cube, though there are integer points. A similar two-sided example is constructed in dimension $37$. We consider possible locations of empty quadrics with respect to vertices of the cube, which is a particular case of a discrete optimization problem for a quadratic polynomial on the set of vertices of the cube. We demonstrate existence of a large number of pairs of parallel hyperplanes such that each pair contains a large number of points of a prescribed set.

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English version:
Problems of Information Transmission, 2012, 48:2, 185–192

Bibliographic databases:

Document Type: Article
UDC: 621.391.1+519.146
Received: 15.11.2011
Revised: 23.01.2012

Citation: K. Yu. Gorbunov, A. V. Seliverstov, V. A. Lyubetsky, “Geometric relationship between parallel hyperplanes, quadrics, and vertices of a hypercube”, Probl. Peredachi Inf., 48:2 (2012), 113–120; Problems Inform. Transmission, 48:2 (2012), 185–192

Citation in format AMSBIB
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\by K.~Yu.~Gorbunov, A.~V.~Seliverstov, V.~A.~Lyubetsky
\paper Geometric relationship between parallel hyperplanes, quadrics, and vertices of a~hypercube
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 2
\pages 113--120
\mathnet{http://mi.mathnet.ru/ppi2079}
\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 2
\pages 185--192
\crossref{https://doi.org/10.1134/S0032946012020081}
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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. V. Seliverstov, “On monomials in quadratic forms”, J. Appl. Industr. Math., 7:3 (2013), 431–434  mathnet  crossref  mathscinet
    2. A. V. Seliverstov, “Mnogogranniki i svyaznye podgrafy”, Diskretn. analiz i issled. oper., 21:3 (2014), 82–86  mathnet  mathscinet
  • Проблемы передачи информации Problems of Information Transmission
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