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Geometriae Dedicata

, Volume 29, Issue 3, pp 311–315 | Cite as

Matroids without adjoint

  • Achim Bachem
  • Alfred Wanka
Article

Abstract

The purpose of this note is to give an example of a rank-4 matroid which not only shows that Levi's intersection property is not a sufficient condition for the existence of an adjoint but also seems to have an interesting structure of the lattice of flats.

Keywords

Extension Lattice Separation Theorem Oriented Matroids Geometric Lattice Extension Equivalence 
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

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    Alfter, M., Kern, W. and Wanka, A., ‘On Adjoints and Dual Matroids’, Working Paper WP 88.49, Mathematisches Institut, University of Cologne, Cologne, 1988.MATHGoogle Scholar
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    Bachem, A. and Kern, W., ‘Extension Equivalence of Oriented Matroids’,Euro. J. Comb. 7 (1986).Google Scholar
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    Bachem, A. and Wanka, A., ‘Euclidean Intersection Properties’ (to appear inJournal of Combinatorical Theory).Google Scholar
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    Crapo, H. H. and Rota, G. C., ‘On the Foundation of Combinatorial Theory’,Combinatorial Geometries, MIT Press, London, 1970.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Achim Bachem
    • 1
  • Alfred Wanka
    • 1
  1. 1.Mathematisches InstitutUniversität KölnKöln 41Germany

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