Geodesic
Empty Simplices in Euclidean Space
Canadian mathematical bulletin, Tome 30 (1987) no. 4, pp. 436-445

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DOI

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 P n is given with , where K(d) is a constant depending only on d. Several related questions are investigated.
DOI : 10.4153/CMB-1987-064-1
Mots-clés : Primary 52A37, Secondary 10K30 
Bárány, Imre; Füredi, Zoltán. Empty Simplices in Euclidean Space. Canadian mathematical bulletin, Tome 30 (1987) no. 4, pp. 436-445. doi: 10.4153/CMB-1987-064-1
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