6 papers
Palindromicity of multivariate Eulerian polynomials
Alejandro González Nevado
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice…
The generalized Lax conjecture is true for topological reasons related to compactness, convexity and determinantal deformations of increasing products of pointwise approximating linear forms
Alejandro González Nevado
We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigi…
A Method for Establishing Asymptotically Accurate Bounds for Extremal Roots of Eulerian Polynomials Using Polynomial Stability Preservers
Alejandro González Nevado
We develop the tools to bound extreme roots of multivariate real zero polynomials globally. This is done through the use of a relaxation that approximates their rigidly convex sets…
Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets
Alejandro González Nevado
Stable multivariate Eulerian polynomials were introduced by Brändén. Particularizing some variables, it is possible to extract real zero multivariate Eulerian polynomials from th…
Spectrahedral relaxations of Eulerian rigidly convex sets
Alejandro González Nevado
We study a generalization of Eulerian polynomials to the multivariate setting introduced by Brändén. Although initially these polynomials were introduced using the language of hy…
Order Structures around Evolution Algebras
Alejandro González Nevado
We consider evolution algebras and their related substructures: evolution ideals and evolution subalgebras. After exposing some of the concepts related to them in the literature, w…