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  • 1
    Electronic Resource
    Electronic Resource
    Random polytopes in thed-dimensional cube (1986)
    Springer
    Discrete & computational geometry 1 (1986), S. 315-319 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetC d be the set of vertices of ad-dimensional cube,C d ={(x 1, ...,x d ):x i =±1}. Let us choose a randomn-element subsetA(n) ofC d . Here we prove that Prob (the origin belongs to the convA(2d+x→2d))=φ(x)+o(1) ifx is fixed andd → ∞. That is, for an arbitraryε〉0 the convex hull of more than (2+ε)d vertices almost always contains 0 while the convex hull of less than (2-ε)d points almost always avoids it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187704
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the kernel of intersecting families (1987)
    Springer
    Graphs and combinatorics 3 (1987), S. 91-94 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Letℱ be at-wises-intersecting family, i.e.,|F 1 ∩ ... ∩ F t | ≥ s holds for everyt members ofℱ. Then there exists a setY such that|F 1 ∩ ... ∩ F t ∩ Y| ≥ s still holds for everyF 1,...,F t ∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes ofY.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788533
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Bounding one-way differences (1987)
    Springer
    Graphs and combinatorics 3 (1987), S. 341-347 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Letf(n, k) denote the maximum length of a sequence (F 1,F 2,...) of distinct subsets of ann-element set with the property that|F i ∖F j | 〈 k for alli 〈 j. We determine the exact values off(n, 2) and characterize all the extremal sequences. Fork ≥ 3 we prove that $$f(n,k) = (1 + o(1))\left( {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right)$$ . Some related problems are also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788556
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Legitimate colorings of projective planes (1989)
    Springer
    Graphs and combinatorics 5 (1989), S. 95-106 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For a projective plane ℙ n of ordern, letϰ(ℙ n ) denote the minimum numberk, so that there is a coloring of the points of ℙ n ink colors such that no two distinct lines contain precisely the same number of points of each color. Answering a question of A. Rosa, we show that for all sufficiently largen, 5 ≤ϰ(ℙ n ) ≤ 8 for every projective plane ℙ n of ordern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788662
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Colouring finite incidence structures (1986)
    Springer
    Graphs and combinatorics 2 (1986), S. 339-346 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract One of our results: Let ℙ denote a finite projective plane of ordern. Colour its vertices byχ colours. If no colour appears more than twice on any of the lines, thenχ ≥ n + 1. Explicit constructions show that this bound is sharp when ℙ is desarguesian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788107
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    On the dimensions of ordered sets of bounded degree (1986)
    Springer
    Order 3 (1986), S. 15-20 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be a partially ordered set. Define k = k (P) = max p∈ |{x ∈ P : p 〈 x or p = x}|, i.e., every element is comparable with at most k others. Here it is proven that there exists a constant c (c 〈 50) such that dim P 〈 ck(log k)2. This improves an earlier result of Rödl and Trotter (dim P ≤2 k 2+2). Our proof is nonconstructive, depending in part on Lovász' local lemma.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00403406
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  • 7
    Electronic Resource
    Electronic Resource
    The jump number of suborders of the power set order (1989)
    Springer
    Order 6 (1989), S. 101-103 
    Details
    ISSN: 1572-9273
    Keywords: Primary 06A10 ; secondary 68C25 ; Jump number ; power set order ; Boolean lattice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be an ordered set induced by several levels of a power set. We give a formula for the jump number of P and show that reverse lexicographic orderings of P are optimal. The proof is based on an extremal set result of Frankl and Kalai.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00341640
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    The number of triangles covering the center of an n-set (1984)
    Springer
    Geometriae dedicata 17 (1984), S. 69-77 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let the points P 1, P 2, ..., P nbe given in the plane such that there are no three on a line. Then there exists a point of the plane which is contained in at least n 3/27 (open) P iPjPktriangles. This bound is the best possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181519
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Nonexistence of universal graphs without some trees (1997)
    Springer
    Combinatorica 17 (1997), S. 163-171 
    Details
    ISSN: 1439-6912
    Keywords: 05C10 ; 05C60 ; 05C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract IfG is a finite tree with a unique vertex of largest, and ≥4 degree which is adjacent to a leaf then there is no universal countableG-free graph.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01200905
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  • 10
    Electronic Resource
    Electronic Resource
    On the number of halving planes (1990)
    Springer
    Combinatorica 10 (1990), S. 175-183 
    Details
    ISSN: 1439-6912
    Keywords: 52 A 37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetS ⊂ℝ3 be ann-set in general position. A plane containing three of the points is called a halving plane if it dissectsS into two parts of equal cardinality. It is proved that the number of halving planes is at mostO(n 2.998). As a main tool, for every setY ofn points in the plane a setN of sizeO(n 4) is constructed such that the points ofN are distributed almost evenly in the triangles determined byY.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123008
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    Paper (German National Licenses)
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