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Algebra Discrete Math., 2010, Volume 10, Issue 1, Pages 1–7 (Mi adm35)  

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

RESEARCH ARTICLE

Partitions of groups and matroids into independent subsets

Taras Banakha, Igor Protasovb

a Department of Mathematics, Ivan Franko National University of Lviv, Universytetska 1, 79000 Lviv, Ukraine
b Department of Cybernetics, Kyiv National University, Volodymyrska 64, 01033 Kyiv, Ukraine

Abstract: Can the set $\mathbb R\setminus\{0\}$ be covered by countably many linearly (algebraically) independent subsets over the field $\mathbb Q$? We use a matroid approach to show that an answer is “Yes” under the Continuum Hypothesis, and “No” under its negation.

Keywords: matroid, partition, independent subset.

Full text: PDF file (201 kB)

Bibliographic databases:
MSC: 05B35, 05A18
Received: 04.10.2010
Revised: 04.10.2010
Language:

Citation: Taras Banakh, Igor Protasov, “Partitions of groups and matroids into independent subsets”, Algebra Discrete Math., 10:1 (2010), 1–7

Citation in format AMSBIB
\Bibitem{BanPro10}
\by Taras Banakh, Igor Protasov
\paper Partitions of groups and matroids into independent subsets
\jour Algebra Discrete Math.
\yr 2010
\vol 10
\issue 1
\pages 1--7
\mathnet{http://mi.mathnet.ru/adm35}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2807683}
\zmath{https://zbmath.org/?q=an:1224.05084}


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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. Igor Protasov, “Partitions of groups into thin subsets”, Algebra Discrete Math., 11:2 (2011), 78–81  mathnet  mathscinet  zmath
    2. Igor Protasov, “Partitions of groups into sparse subsets”, Algebra Discrete Math., 13:1 (2012), 107–110  mathnet  mathscinet  zmath
    3. Protasov I., Slobodianiuk S., “Partitions of Groups”, Adv. Appl. Discret. Math., 15:1 (2015), 33–60  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
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