vix.ing · top · new · best · stats · spec

Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming

2022/06/06 by Papri Dey, Dey, Papri
Mathematics · #05E14 #05E99 #14P99 #15A15 #52A20 #90C25 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2206.02759

openalex publication_date 2022/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 k-locally singular matrices via hyperbolic programming.

Related