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FOURTH
INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Carnegie Mellon University

Pittsburgh, PA, USA

July 20-23 2005

#
ISIPTA'05 ELECTRONIC PROCEEDINGS

## Anton Wallner

# Maximal Number of Vertices of Polytopes Defined by F-Probabilities

### Abstract

Every F-probability (= coherent probability) FF on a finite sample space
Omega_k with k elements defines a set of classical probabilities in
accordance with the interval limits. This set, called ``structure'' of FF,
is a convex polytope having dimension <= k-1. We prove that the maximal
number of vertices of structures is exactly k!.

** Keywords. ** Geometry of interval probability, number of vertices of structures/cores/credal sets, combinatorial theory of polyhedra, 0/1-matrices.

** Paper Download **

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** Authors addresses: **

Institut fuer Statistik

Ludwig-Maximilians-Universitaet Muenchen

Ludwigstr. 33

80539 Muenchen

** E-mail addresses: **

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