Using a multivariate spectrahedral relaxation for Eulerian polynomials produces root bounds that strictly beat the best univariate relaxation bound, but only by an exponentially small amount.
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Spectrahedral relaxations of Eulerian rigidly convex sets
Using a multivariate spectrahedral relaxation for Eulerian polynomials produces root bounds that strictly beat the best univariate relaxation bound, but only by an exponentially small amount.