On a polynomial positivity question of Collins, Dykema, and Torres-Ayala related to the Bessis-Moussa-Villani Conjecture

TL;DR

This paper constructs sum of squares certificates to prove non-negativity of specific polynomial families related to a reformulation of the Bessis-Moussa-Villani conjecture, advancing understanding of polynomial positivity.

Contribution

It introduces new sum of squares certificates for polynomials connected to a variant of the Bessis-Moussa-Villani conjecture, providing a novel approach to polynomial positivity.

Findings

Sum of squares certificates established for specific polynomial families

Non-negativity of these polynomials verified through these certificates

Progress towards the polynomial positivity aspect of the Bessis-Moussa-Villani conjecture

Abstract

We construct sum of squares certificates of non-negativity for two families of polynomials appearing as a variant by Collins, Dykema, and Torres-Ayala to H\"aegele's reformulation of a conjecture by Bessis, Moussa, and Villani.