发表机构
University of Wisconsin–Madison; ShanghaiTech University（威斯康星大学麦迪逊分校; 上海科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三元洛伦兹多项式归一化系数的有界比率与最优界常数，通过Hessian切片给出显式表示，并推广至四元情形，最终与体积多项式及拟阵基轮廓的界进行比较。
AI 中文摘要
我们研究三元洛伦兹多项式的归一化系数之间的有界比率和最优界常数。对于每个固定的 $M$-凸支撑且任意次数，我们给出了有界比率锥关于二次Hessian切片的显式表示。我们进一步证明，相同的局部到全局原理对四元三次多项式成立，但对全支撑四元四次多项式不成立。然后，我们通过一个变分公式表达最优界常数，该公式结合了局部支撑函数与切片之间的线性相容性约束。对于全支撑情形，我们在任意次数下确定了所有相容性关系；在三次情形，这为每个双生成元截面给出了显式的最优常数。最后，我们将所得的洛伦兹界与体积多项式和秩三拟阵基轮廓的界进行比较。
英文摘要
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.
Comments22 pages, we added D. Soskin's important observations to Remark 3.10 and included a declaration regarding the use of AI
