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Bounded Ratios of Lorentzian Polynomials I: The Ternary Theory and Optimal Bounding Constants

Year: 2026

Type: preprint

Abstract: We study bounded ratios and optimal bounding constants among the normalized coefficients of ternary Lorentzian polynomials. For every fixed $M$-convex support and in arbitrary degree, we give an explicit presentation of the bounded-ratio cone in terms of quadratic Hessian slices. We then express the optimal bounding constants through a variational formula combining local support functions with linear compatibility constraints between slices. For full support, we determine all compatibility relations in arbitrary degree; in degree three, this yields explicit optimal constants for every two-generator section. Finally, we compare the resulting Lorentzian bounds with those for volume polynomials and rank-three matroid basis profiles.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.06145

Authors: Chen, Dijia, Gan, Bowen, Liu, Ivy, Wang, Zemeng, Wu, Chengzhi

Institution: University of Wisconsin–Madison

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Wisconsin-Madison, ShanghaiTech University, Division of Mathematical Sciences

OpenAlex ID: W7212037447

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