Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    A Positive Fraction Erdos - Szekeres Theorem (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 335-342 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We prove a fractional version of the Erdős—Szekeres theorem: for any k there is a constant c k 〉 0 such that any sufficiently large finite set X⊂ R 2 contains k subsets Y 1 , ... ,Y k , each of size ≥ c k |X| , such that every set {y 1 ,...,y k } with y i ε Y i is in convex position. The main tool is a lemma stating that any finite set X⊂ R d contains ``large'' subsets Y 1 ,...,Y k such that all sets {y 1 ,...,y k } with y i ε Y i have the same geometric (order) type. We also prove several related results (e.g., the positive fraction Radon theorem, the positive fraction Tverberg theorem). 〈lsiheader〉 〈onlinepub〉26 June, 1998 〈editor〉Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 〈pdfname〉19n3p335.pdf 〈pdfexist〉yes 〈htmlexist〉no 〈htmlfexist〉no 〈texexist〉yes 〈sectionname〉 〈/lsiheader〉
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009350
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    A combinatorial property of points and ellipsoids (1990)
    Springer
    Discrete & computational geometry 5 (1990), S. 375-382 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For eachd≥1 there is a constantc d〉0 such that any finite setX⊂R d contains a subsetYχX, |Y|≤[1/4d(d+3)]+1 having the following property: ifE⊃Y is an ellipsoid, then |E ν X|≥c d |X|.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187798
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    A Central Limit Theorem for Convex Chains in the Square (2000)
    Springer
    Discrete & computational geometry 23 (2000), S. 35-50 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Points P 1 ,... ,P n in the unit square define a convex n -chain if they are below y=x and, together with P 0 =(0,0) and P n+1 =(1,1) , they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature is that the limit shape is a direct consequence of the method. The main result is an accompanying central limit theorem for these chains. A weak convergence result implies several other statements concerning the deviations between random convex chains and their limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009490
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A combinatorial result about points and balls in euclidean space (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 259-262 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For eachn≥1 there isc n 〉0 such that for any finite sexX ⊆ ℝ″ there isA ⊆X, |A|≤1/2(n+3), having the following property: ifB ⊇A is ann-ball, then |B ∩X|≥c n |X|. This generalizes a theorem of Neumann-Lara and Urrutia which states thatc 2≥1/60.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187727
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Classification of two-person ordinal bimatrix games (1992)
    Springer
    International journal of game theory 21 (1992), S. 267-290 
    Details
    ISSN: 1432-1270
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The set of possible outcomes of a strongly ordinal bimatrix games is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto-optimal sets of each cardinality; we establish asymptotic bounds for the number of different convex hulls of the point sets, for the average shape of the set of points dominated by the Pareto-optimal set, and for the average shape of the convex hull of the point set. We also indicate the effect of individual rationality considerations on our results. As most of our results are asymptotic, the appendix includes a careful examination of the important case of 2×2 games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01258279
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On the number of convex lattice polytopes (1992)
    Springer
    Geometric and functional analysis 2 (1992), S. 381-393 
    Details
    ISSN: 1420-8970
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01896660
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Borsuk's theorem and the number of facets of centrally symmetric polytopes (1982)
    Springer
    Acta mathematica hungarica 40 (1982), S. 323-329 
    Details
    ISSN: 1588-2632
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01903592
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...