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  • 52 A 20  (1)
  • Simplicial complexes  (1)
  • 1
    Electronic Resource
    Electronic Resource
    The topological structure of maximal lattice free convex bodies: The general case (1998)
    Springer
    Mathematical programming 80 (1998), S. 1-15 
    Details
    ISSN: 1436-4646
    Keywords: Minimal test sets for integer programming ; Simplicial complexes ; Maximal lattice free bodies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a genericm × n matrixA, the simplicial complexK(A) is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form {x : Ax ⩽ b}. The main result of this paper is that the topological space associated withK(A) is homeomorphic withR m−1 . © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582128
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The caratheodory number for thek-core (1990)
    Springer
    Combinatorica 10 (1990), S. 185-194 
    Details
    ISSN: 1439-6912
    Keywords: 52 A 20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Thek-core of the setS ⊂ℝ n is the intersection of the convex hull of all setsA ⊆ S with ¦S∖A¦〈-k. The Caratheodory number of thek-core is the smallest integerf (d,k) with the property thatx ∈ core kS, S ⊂ℝ n implies the existence of a subsetT ⊆ S such thatx ∈ corekT and ¦T¦≤f (d, k). In this paper various properties off(d, k) are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123009
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    Paper (German National Licenses)
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