Spectrahedrality of hyperbolicity cones of multivariate matching polynomials

• The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Branden). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Generalized Lax conjecture

Hyperbolic polynomial

Stable polynomial

Multivariate matching polynomial

Multivariate independence polynomial

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