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Empty Simplices in Euclidean Space

Published online by Cambridge University Press:  20 November 2018

Imre Bárány  and
Zoltán Füredi
Imre Bárány
Affiliation:
Or, Cornell University Ithaca, NY 14853
Zoltán Füredi
Affiliation:
Rutcor, Rutgers University New Brunswick, NJ 08903
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Abstract

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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.

Keywords

Primary 52A37Secondary 10K30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 436 - 445
Copyright
Copyright © Canadian Mathematical Society 1987

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