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, Volume 5, Issue 1, pp 23–32 | Cite as

Combinatorial representation and convex dimension of convex geometries

  • Paul H. Edelman
  • Michael E. Saks
Article

Abstract

We develop a representation theory for convex geometries and meet distributive lattices in the spirit of Birkhoff's theorem characterizing distributive lattices. The results imply that every convex geometry on a set X has a canonical representation as a poset labelled by elements of X. These results are related to recent work of Korte and Lovász on antimatroids. We also compute the convex dimension of a convex geometry.

AMS subject classifications (1980)

06A10 06B05 

Key words

Meet distributive lattices convex geometries convex dimension 

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References

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Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Paul H. Edelman
    • 1
  • Michael E. Saks
    • 3
    • 4
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA
  4. 4.Bell Communications ResearchMorristownUSA

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