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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{chen2026bounded,
  title = {{Bounded Ratios of Lorentzian Polynomials I: The Ternary Theory and Optimal Bounding Constants}},
  author = {Dijia Chen and Bowen Gan and Ivy Liu and Zemeng Wang and Chengzhi Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06145},
  eprint = {2609.06145},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06145},
}
RIS
TY  - UNPB
TI  - Bounded Ratios of Lorentzian Polynomials I: The Ternary Theory and Optimal Bounding Constants
AU  - Dijia Chen
AU  - Bowen Gan
AU  - Ivy Liu
AU  - Zemeng Wang
AU  - Chengzhi Wu
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.06145
UR  - https://arxiv.org/abs/2609.06145
AB  - 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.
ER  -