Series-parallel extensions and Ehrhart positivity

@misc{li2026seriesparallel,
  title = {{Series-parallel extensions and Ehrhart positivity}},
  author = {Yao Li and Sihong Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03122},
  eprint = {2610.03122},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03122},
}

TY  - UNPB
TI  - Series-parallel extensions and Ehrhart positivity
AU  - Yao Li
AU  - Sihong Shao
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03122
UR  - https://arxiv.org/abs/2610.03122
AB  - We prove Ehrhart positivity for series-parallel matroids and extend this result to all series-parallel extensions of multi-path matroids. A formula for the Ehrhart coefficients of series-parallel matroids is derived and used to prove strict positivity. An extension criterion based on weighted lattice-point counts is established. Recursive formulas for lattice-point counts are derived, and the recursion is shown to preserve a class of polynomials with nonnegative coefficients. We finally construct a connected transversal matroid with a negative Ehrhart coefficient, disproving the conjecture of Ferroni, Morales, and Panova that every connected matroid whose base polytope admits a subdivision into series-parallel matroid base polytopes is Ehrhart positive.
ER  -