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International Conference on Formal Concept Analysis

ICFCA 2007: Formal Concept Analysis pp 313–327Cite as

Bipartite Ferrers-Graphs and Planar Concept Lattices

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 4390)

Abstract

There exists a close relation between the Ferrers-dimension of a context and the order dimension of the appropriate concept lattice [4]. Based on this fact we will introduce Ferrers-Graphs on contexts and show how they characterize planar concept lattices.

Keywords

  • Bipartite Graph
  • Concept Lattice
  • Lattice Element
  • Order Dimension
  • Formal Concept Analysis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Baker, K.A., Fishburn, P., Roberts, F.S.: Partial Orders of Dimension 2. Networks 2, 11–28 (1971)

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  2. Birkhoff, G.: Lattice Theory, 3rd edn. Amer. Math. Soc., New York (1967)

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  3. Dushnik, B., Miller, E.W.: Partially Ordered Sets. Amer. J. Math. 63, 600–610 (1941)

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  4. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)

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  5. Private communication with B. Ganter

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  6. Reuter, K.: Removing Critical Pairs. Preprint, no. 1241, TU Darmstadt (1989)

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  7. Zschalig, C.: Planarity of Lattices - An approach based on attribute additivity. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 391–402. Springer, Heidelberg (2005)

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  8. Zschalig, C.: Characterizing Planar Lattices Using Left-relations. In: Missaoui, R., Schmidt, J. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3874, pp. 280–290. Springer, Heidelberg (2006)

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Author information

Authors and Affiliations

  1. Institut für Algebra, TU Dresden, Germany

    Christian Zschalig

Authors
  1. Christian Zschalig
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Editor information

Sergei O. Kuznetsov Stefan Schmidt

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© 2007 Springer Berlin Heidelberg

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Cite this paper

Zschalig, C. (2007). Bipartite Ferrers-Graphs and Planar Concept Lattices. In: Kuznetsov, S.O., Schmidt, S. (eds) Formal Concept Analysis. ICFCA 2007. Lecture Notes in Computer Science(), vol 4390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70901-5_20

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  • DOI: https://doi.org/10.1007/978-3-540-70901-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70828-5

  • Online ISBN: 978-3-540-70901-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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