Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find




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

Izvestiya: Mathematics, 2005, Volume 69, Issue 3, Pages 513–537
DOI: https://doi.org/10.1070/IM2005v069n03ABEH000537 (Mi im641) 		 
This article is cited in 21 scientific papers (total in 21 papers)

The problems of Borsuk and Grünbaum on lattice polytopes

A. M. Raigorodskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (341 kB) Citations (21) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/IM2005v069n03ABEH000537
Abstract: We study two classical problems of combinatorial geometry, the Borsuk problem on partitioning sets into parts of smaller diameter and the Grünbaum problem on covering sets by balls. We obtain new non-trivial upper bounds for the minimum number of parts of smaller diameter into which an arbitrary lattice polytope can be partitioned, as well as for the minimum number of balls of the same diameter by which any such polytope can be covered.
Received: 01.10.2003
Bibliographic databases:
UDC: 514.17+519.174
MSC: 52B20, 05C15, 05D15
Language: English
Original paper language: Russian
Citation: A. M. Raigorodskii, “The problems of Borsuk and Grünbaum on lattice polytopes”, Izv. Math., 69:3 (2005), 513–537
Citation in format AMSBIB
\Bibitem{Rai05}
\by A.~M.~Raigorodskii
\paper The problems of Borsuk and Gr\"unbaum on lattice polytopes
\jour Izv. Math.
\yr 2005
\vol 69
\issue 3
\pages 513--537
\mathnet{http://mi.mathnet.ru//eng/im641}
\crossref{https://doi.org/10.1070/IM2005v069n03ABEH000537}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2150502}
\zmath{https://zbmath.org/?q=an:1153.52301}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000231192200003}
\elib{https://elibrary.ru/item.asp?id=9176284}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645455244}
Linking options:
  • https://www.mathnet.ru/eng/im641
  • https://doi.org/10.1070/IM2005v069n03ABEH000537
  • https://www.mathnet.ru/eng/im/v69/i3/p81
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024