Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming
Algebraic Geometry
2025-03-24 v4 Combinatorics
Abstract
We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and conic stable polynomials belong to this class, and the set of polynomials with Lorentzian signature is closed. Finally, we develop a method for computing permanents of nonsingular matrices which belong to a class that includes nonsingular -locally singular matrices via hyperbolic programming.
Cite
@article{arxiv.2206.02759,
title = {Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming},
author = {Papri Dey},
journal= {arXiv preprint arXiv:2206.02759},
year = {2025}
}
Comments
Theorem 42 is incorrect, and the concept of polynomials with Lorentzian signature has been further developed as K-Lorentzian polynomials in recent or follow-up papers