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Ehrhart positivity for lattice path matroids

  • Luis Ferroni
  • Alejandro H. Morales
  • Greta Panova
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Abstract

We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order polynomials of fences. Our main result supports the conjecture by Ferroni, Jochemko, and Schröter (2022) on the Ehrhart positivity of positroids. Furthermore, our main result implies that all Schubert matroids are Ehrhart positive, which thus settles a conjecture by Fan and Li (2024), and shows Newton polytopes of certain Schubert and key polynomials are Ehrhart positive.

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Cite

BibTeXRIS
BibTeX
@misc{ferroni2026ehrhart,
  title = {{Ehrhart positivity for lattice path matroids}},
  author = {Luis Ferroni and Alejandro H. Morales and Greta Panova},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.22673},
  eprint = {2605.22673},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.22673},
}
RIS
TY  - UNPB
TI  - Ehrhart positivity for lattice path matroids
AU  - Luis Ferroni
AU  - Alejandro H. Morales
AU  - Greta Panova
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2605.22673
UR  - https://arxiv.org/abs/2605.22673
AB  - We prove that all lattice path matroids are Ehrhart positive. This unifies and generalizes numerous results on the Ehrhart positivity of matroids developed over the last two decades. We rely on our previous work on the positivity of order polynomials of fences. Our main result supports the conjecture by Ferroni, Jochemko, and Schröter (2022) on the Ehrhart positivity of positroids. Furthermore, our main result implies that all Schubert matroids are Ehrhart positive, which thus settles a conjecture by Fan and Li (2024), and shows Newton polytopes of certain Schubert and key polynomials are Ehrhart positive.
ER  -