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  • 1
    Electronic Resource
    Electronic Resource
    On the Cocircuit Graph of an Oriented Matroid (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 257-266 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. In this paper we consider the cocircuit graph G M of an oriented matroid M , the 1 -skeleton of the cell complex W formed by the span of the cocircuits of M . In general, W is not determined by G M . However, we show that if the vertex set (resp. edge set) of G M is properly labeled by the hyperplanes (resp. colines) of M , G M determines W . Also we prove that, when M is uniform, the cocircuit graph together with all antipodal pairs of vertices being marked determines W . These results can be considered as variations of Blind—Mani's theorem that says the 1-skeleton of a simple convex polytope determines its face lattice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010031
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the Generation of Oriented Matroids (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 197-208 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We provide a multiple purpose algorithm for generating oriented matroids. An application disproves a conjecture of Grünbaum that every closed triangulated orientable 2-manifold can be embedded geometrically in R 3 , i.e., with flat triangles and without self-intersections. We can show in particular that there exists an infinite class of orientable triangulated closed 2-manifolds for each genus g \geq 6 that cannot be embedded geometrically in Euclidean 3-space. Our algorithm is interesting in its own right as a tool for many investigations in which oriented matroids play a key role.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010027
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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