Abstract
The set of nonnegative solutions of a system of linear equations or inequalities is a convex polyhedron. If the coefficients of the system are chosen at random, the number of vertices of this polyhedron is a random variable. Its expected value, dependent on the probability distribution of the coefficients, which are assumed to be nonnegative throughout, is investigated, and a distribution-independent upper bound for this expected value is established.
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Buchta, C. On nonnegative solutions of random systems of linear inequalities. Discrete Comput Geom 2, 85–95 (1987). https://doi.org/10.1007/BF02187872
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DOI: https://doi.org/10.1007/BF02187872