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PreprintCC BY 4.0arXiv

Ehrhart positivity for paving positroids

  • Feihu Liu
  • Zihao Zhang
Open at sourcePDFDOICite

Abstract

A central conjecture of Ferroni, Jochemko, and Schröter posits that every positroid is Ehrhart positive. While Ehrhart positivity has recently been verified for notable classes such as lattice path matroids and series-parallel matroids, the general conjecture remains open. In this paper, we prove that the base polytope of any paving positroid has positive Ehrhart coefficients. This establishes a new class of Ehrhart positive positroids and provides substantial evidence supporting this conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026ehrhart,
  title = {{Ehrhart positivity for paving positroids}},
  author = {Feihu Liu and Zihao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21501},
  eprint = {2610.21501},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21501},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ehrhart positivity for paving positroids
AU  - Feihu Liu
AU  - Zihao Zhang
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.21501
UR  - https://arxiv.org/abs/2610.21501
AB  - A central conjecture of Ferroni, Jochemko, and Schröter posits that every positroid is Ehrhart positive. While Ehrhart positivity has recently been verified for notable classes such as lattice path matroids and series-parallel matroids, the general conjecture remains open. In this paper, we prove that the base polytope of any paving positroid has positive Ehrhart coefficients. This establishes a new class of Ehrhart positive positroids and provides substantial evidence supporting this conjecture.
ER  -