Combinatorial representation and convex dimension of convex geometries View Full Text


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Article Info

DATE

1988-03

AUTHORS

Paul H. Edelman, Michael E. Saks

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. More... »

PAGES

23-32

References to SciGraph publications

  • 1985-12. The theory of convex geometries in GEOMETRIAE DEDICATA
  • 1982. Dimension Theory for Ordered Sets in ORDERED SETS
  • 1980-12. Meet-distributive lattices and the anti-exchange closure in ALGEBRA UNIVERSALIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00143895

    DOI

    http://dx.doi.org/10.1007/bf00143895

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1041492674


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