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arXiv · 2609.06145

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

Dijia Chen·Bowen Gan·Ivy Liu·Zemeng Wang·Chengzhi Wu
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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.

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Dijia Chen, Bowen Gan, Ivy Liu, Zemeng Wang, Chengzhi Wu. 2026-09-14. Bounded Ratios of Lorentzian Polynomials I: The Ternary Theory and Optimal Bounding Constants. https://arxiv.org/abs/2609.06145

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