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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

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1337-2211
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Volume 65, Issue 1

Issues

On Systems of Independent Sets

Pavel Jahoda
  • Department of Applied Mathematics VŠB-Technical University of Ostrava 17. listopadu 15/2172 CR–708 33 Ostrava CZECH REPUBLIC
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  • Other articles by this author:
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/ Monika Jahodová
  • Department of Applied Mathematics VŠB-Technical University of Ostrava 17. listopadu 15/2172 CR-708 33 Ostrava CZECH REPUBLIC
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-03-25 | DOI: https://doi.org/10.1515/ms-2015-0004

Abstract

The classical probability that a randomly chosen number from the set {n ∈ N : n ≤ n0} belongs to a set A ⊆ N can be approximated for large number n0 by the asymptotic density of the set A. We say that the events are independent if the probability of their intersection is equal to the product of their probabilities. By analogy we define the independence of sets. We say that the sets are independent if the asymptotic density of their intersection is equal to the product of their asymptotic densities. In the article is described a generalisation of one of the criteria of independence of sets and one interesting case in which sets are not independent

Keywords : asymptotic density; independent sets; independent events

References

  • [1] JAHODA, P.-PĚLUCHOVÁ, M.: Systems of sets with multiplicative asymptotic density, Math. Slovaca 58 (2008), 393-404.Web of ScienceGoogle Scholar

  • [2] JAHODA, P.-JAHODOVÁ, M.: On a set of asymptotic densities, Acta Math. Univ. Ostrav. 16 (2009), 21-30.Google Scholar

  • [3] JAHODOVÁ, M.: Systems of independent sets. Thesis, University of Ostrava, 2011 (Czech). Google Scholar

About the article

Received: 2012-02-21

Accepted: 2012-09-19

Published Online: 2015-03-25

Published in Print: 2015-02-01


Citation Information: Mathematica Slovaca, Volume 65, Issue 1, Pages 33–44, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0004.

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