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Combinatorics hidden in hyperbolic polynomials and related topics

Research paper by Leonid Gurvits

Indexed on: 05 Feb '04Published on: 05 Feb '04Published in: Mathematics - Combinatorics



Abstract

The main topic of this paper is various "hyperbolic" generalizations of the Edmonds-Rado theorem on the rank of intersection of two matroids. We prove several results in this direction and pose a few questions. We also give generalizations of the Obreschkoff theorem and recent results of J. Borcea and B. Shapiro.