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g-Positivity for Paving Matroids
Abstract
We prove that the g-polynomial of every paving matroid has nonnegative coefficients. Our proof combines a deletion-contraction argument with an elementary coefficient inequality for the g-polynomials of uniform matroids.
Related
- Real-rootedness of the Z-polynomials of sparse paving matroids and strict interlacing for uniform matroids
- Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids
- Unimodality of Kazhdan--Lusztig polynomials of sparse paving matroids
- Ehrhart positivity for paving positroids
- Ehrhart positivity for lattice path matroids
BibTeX
@misc{wang2026gpositivity,
title = {{g-Positivity for Paving Matroids}},
author = {Yiyu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30597},
eprint = {2609.30597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30597},
}
RIS
TY - UNPB
TI - g-Positivity for Paving Matroids
AU - Yiyu Wang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30597
UR - https://arxiv.org/abs/2609.30597
AB - We prove that the g-polynomial of every paving matroid has nonnegative coefficients. Our proof combines a deletion-contraction argument with an elementary coefficient inequality for the g-polynomials of uniform matroids.
ER -