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Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
hyperbolic polynomials hyperbolicity cones spectrahedral cones elementary symmetric polynomials spanning trees matrix-tree theorem
2012/4/16
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theore...
New Inequalities Between Elementary Symmetric Polynomials
Elementary Symmetric Polynomials New Inequalities
2008/6/30
New families of sharp inequalities between elementary symmetric polynomials are proven. We estimate above and below by the elementary symmetric polynomials in the case, when are non-negative real n...