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Mat. Zametki, 2000, Volume 68, Issue 6, Pages 830–841 (Mi mz1005)  

This article is cited in 3 scientific papers (total in 3 papers)

A Method of Deducing $L$-Polyhedra for $n$-Lattices

E. P. Baranovskii, P. G. Kononenko

Ivanovo State University

Abstract: We suggest a method for selecting an $L$-simplex in an $L$-polyhedron of an $n$-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an $L$-simplex and by considering a simplex selected from an $L$-polyhedron, we present a new method for describing all types of $L$-polyhedra in lattices of given dimension $n$. We apply the method to deduce all types of $L$-polyhedra in $n$-dimensional lattices for $n=2,3,4$, which are already known from previous results.

DOI: https://doi.org/10.4213/mzm1005

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English version:
Mathematical Notes, 2000, 68:6, 704–712

Bibliographic databases:

UDC: 514.17
Received: 16.04.1998

Citation: E. P. Baranovskii, P. G. Kononenko, “A Method of Deducing $L$-Polyhedra for $n$-Lattices”, Mat. Zametki, 68:6 (2000), 830–841; Math. Notes, 68:6 (2000), 704–712

Citation in format AMSBIB
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\by E.~P.~Baranovskii, P.~G.~Kononenko
\paper A Method of Deducing $L$-Polyhedra for $n$-Lattices
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 6
\pages 830--841
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\crossref{https://doi.org/10.4213/mzm1005}
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\zmath{https://zbmath.org/?q=an:1008.52014}
\elib{http://elibrary.ru/item.asp?id=5021422}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 6
\pages 704--712
\crossref{https://doi.org/10.1023/A:1026648330397}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000166684000021}


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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. P. G. Kononenko, “Affine Types of $L$-Polyhedra for 5-lattices”, Math. Notes, 71:3 (2002), 374–391  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Deza, M, “The hypermetric cone on seven vertices”, Experimental Mathematics, 12:4 (2003), 433  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Dutour, M, “The six-dimensional Delaunay polytopes”, European Journal of Combinatorics, 25:4 (2004), 535  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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