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1 results

  • Empty Simplices in Euclidean Space

  • Imre Bárány, Zoltán Füredi
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 4 / 01 December 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 436-445
    Print publication:
    01 December 1987
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  • Let P - {p1,p2,. . . ,pn} be an independent point-set in ℝd (i.e., there are no d + 1 on a hyperplane). A simplex determined by d + 1 different points of P is called empty if it contains no point of P in its interior. Denote the number of empty simplices in P by fd(P). Katchalski and Meir pointed out that . Here a random construction Pn is given with , where K(d) is a constant depending only on d. Several related questions are investigated.