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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)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2005, Volume 69, Issue 3, Pages 81–108
DOI: https://doi.org/10.4213/im641
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. RAN. Ser. Mat., 69:3 (2005), 81–108; Izv. Math., 69:3 (2005), 513–537
Citation in format AMSBIB
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  • 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
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:648
    Russian version PDF:306
    English version PDF:24
    References:75
    First page:2
     
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