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PreprintCC BY 4.0arXiv

Bounded ratios for Lorentzian polynomials

  • Aayush Bathija
  • Prince Rohatgi
  • Daniel Soskin
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Abstract

We study multiplicative inequalities among the coefficients of Lorentzian polynomials through the notion of bounded ratios. Our main structural result completely characterizes the cone of bounded ratios for Lorentzian polynomials of degree n in k variables. We show that the dual of the cone of bounded ratios is generated by equivalence classes of M-convex functions modulo affine functions. For ternary Lorentzian forms of arbitrary degree n≥3, we show that the cone of bounded ratios is generated by triangular ratios and determine the optimal bounding constant of every bounded ratio. Furthermore, we characterize the pairs (n,k) for which the cone of bounded ratios can be computed by tropicalizing products of n linear forms in k variables with nonnegative coefficients.

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Cite

BibTeXRIS
BibTeX
@misc{bathija2026bounded,
  title = {{Bounded ratios for Lorentzian polynomials}},
  author = {Aayush Bathija and Prince Rohatgi and Daniel Soskin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05341},
  eprint = {2609.05341},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05341},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bounded ratios for Lorentzian polynomials
AU  - Aayush Bathija
AU  - Prince Rohatgi
AU  - Daniel Soskin
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.05341
UR  - https://arxiv.org/abs/2609.05341
AB  - We study multiplicative inequalities among the coefficients of Lorentzian polynomials through the notion of bounded ratios. Our main structural result completely characterizes the cone of bounded ratios for Lorentzian polynomials of degree n in k variables. We show that the dual of the cone of bounded ratios is generated by equivalence classes of M-convex functions modulo affine functions. For ternary Lorentzian forms of arbitrary degree n≥3, we show that the cone of bounded ratios is generated by triangular ratios and determine the optimal bounding constant of every bounded ratio. Furthermore, we characterize the pairs (n,k) for which the cone of bounded ratios can be computed by tropicalizing products of n linear forms in k variables with nonnegative coefficients.
ER  -