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We give explicit polynomial-sized (in $n$ and $k$) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree $k$ in $n$ variables.
An inequality for hyperbolic polynomials
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Semidefinite Optimization and Convex Algebraic Geometry
G. Blekherman, P. A. Parrilo, and R. R. Thomas, editors · 2013
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