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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 233–245
DOI: https://doi.org/10.4213/mzm5188 (Mi mzm5188) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Partition of Three-Dimensional Sets into Five Parts of Smaller Diameter

A. B. Kupavskii, A. M. Raigorodskii

M. V. Lomonosov Moscow State University
Full-text PDF (555 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm5188
Abstract: The classical Borsuk problem on partitioning sets into pieces of smaller diameter is considered. A new upper bound for
$$ d_5^3=\sup_{\Phi\subset\mathbb R^3,\operatorname{diam}\Phi=1}\inf\{x\ge0:\Phi=\Phi_1\cup\Phi_2\cup\dots\cup\Phi_5,\operatorname{diam}\Phi_i\le x\} $$
is given, which improves the previous bound obtained by Lassak in 1982.
Keywords: Borsuk's problem, partition of 3D sets, diameter of a set, Lassak's bound, Gale's conjecture, Jung's ball, Helly's theorem, isometry.
Received: 04.06.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 218–229
DOI: https://doi.org/10.1134/S0001434610010281
Bibliographic databases:
UDC: 514.17
Language: Russian
Citation: A. B. Kupavskii, A. M. Raigorodskii, “Partition of Three-Dimensional Sets into Five Parts of Smaller Diameter”, Mat. Zametki, 87:2 (2010), 233–245; Math. Notes, 87:2 (2010), 218–229
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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