Generating Maximum Members of Independence Systems

  • Reinhardt Euler
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 157)


Given an independence system J over a finite set N= {1,...,n} a relation “ Γ ” is defined for sets X ⊆ N of a fixed cardinality k. This leads to “regular“ systems, which are independence systems having the additional property : Xεj,XΓ => Yε J. The concept of “ Γ -bases” is applied and a criterion to recognize regular systems having matroidal structure is developed. Based on these results an algorithm for the construction of all Γ -bases of independence or regular systems is introduced.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Reinhardt Euler
    • 1
  1. 1.Institut für Ökonometrie und Operations ResearchUniversität BonnBonnGermany

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