P. G. Kononenko, “Affine Types of $L$-Polyhedra for 5-lattices”, Mat. Zametki, 71:3 (2002), 412–430; Math. Notes, 71:3 (2002), 374

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2002, Volume 71, Issue 3, Pages 412–430
DOI: https://doi.org/10.4213/mzm356 (Mi mzm356)

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

Affine Types of

L

$L$ -Polyhedra for 5-lattices

P. G. Kononenko

Ivanovo State University

Full-text PDF (296 kB) Citations (3)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm356

Abstract: We construct an algorithm for deducing all affinely nonequivalent types of

L

$L$ -polyhedra on

n

$n$ -lattices, where

$n\le 5$ . The computational part of the algorithm designed for calculations on a personal computer is based on the relationship between the geometry of lattices and the theory of hypermetric spaces. For the first time, a complete list of affine types (139 types) of

$L$ -polyhedra on 5-lattices is obtained.

Received: 26.04.1999
Revised: 10.10.2001

English version:
Mathematical Notes, 2002, Volume 71, Issue 3, Pages 374–391
DOI: https://doi.org/10.1023/A:1014803008920

Bibliographic databases:

UDC: 514.174.6+519.112.7

Language: Russian

Citation: P. G. Kononenko, “Affine Types of

$L$ -Polyhedra for 5-lattices”, Mat. Zametki, 71:3 (2002), 412–430; Math. Notes, 71:3 (2002), 374–391

Citation in format AMSBIB

\Bibitem{Kon02}

\by P.~G.~Kononenko

\paper Affine Types of $L$-Polyhedra for 5-lattices

\jour Mat. Zametki

\yr 2002

\vol 71

\issue 3

\pages 412--430

\mathnet{http://mi.mathnet.ru/mzm356}

\crossref{https://doi.org/10.4213/mzm356}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1913611}

\zmath{https://zbmath.org/?q=an:1040.52004}

\elib{https://elibrary.ru/item.asp?id=5025285}

\transl

\jour Math. Notes

\yr 2002

\vol 71

\issue 3

\pages 374--391

\crossref{https://doi.org/10.1023/A:1014803008920}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000175483000008}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0141848552}

Linking options:

https://www.mathnet.ru/eng/mzm356

https://doi.org/10.4213/mzm356

https://www.mathnet.ru/eng/mzm/v71/i3/p412

This publication is cited in the following 3 articles:

Sikiric M.D. Garber A. Schuermann A. Waldmann C., “The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices”, Acta Crystallogr. Sect. A, 72:6 (2016), 673–683
Dutour M., “The six-dimensional Delaunay polytopes”, European J. Combin., 25:4 (2004), 535–548
Deza M., Dutour M., “The hypermetric cone on seven vertices”, Experiment. Math., 12:4 (2003), 433–440

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	532
Full-text PDF :	214
References:	84
First page:	1

Registration to the website

Logotypes