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A note on Sylvester's problem for random polytopes in a convex body
Campi, Stefano
Colesanti, Andrea
Gronchi, Paolo
1999
Abstract
For any d-dimensional convex body K of unit volume, d$\geq$2, let
M$_{r}$(K; n), r $\geq$ l, n$\geq$ d+ l, be the r-th order moment
of the volume of the convex hull of n random points from K. The paper
deals with the problem of determining maximizers of M$_{r}$ ( K;
n) in the class of all d-dimensional convex bodies of unit volume.
A method for selecting possible solutions, which is based on special
continuous movements of convex bodies, is presented. The results obtained
by this method support the conjecture that, for every r and n, the
only maximizers of M$_{r}$(K; n) are simplices.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (1999)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
S. Campi, A. Colesanti and P. Gronchi, "A note on Sylvester's problem for random polytopes in a convex body", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (1999), pp. 79-94.
Languages
en
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