Year: 2026
Type: preprint
Abstract: Using the Hodge-Riemann relations for matroid Chow rings, we establish a weighted inequality for flats of a loopless matroid. As applications, we prove the points-lines-planes conjecture and Brylawski's conjecture on the ultra-log-concavity of Whitney numbers of the first kind. We also characterize the cases of equality in both inequalities.
Source: arXiv (Cornell University)
Authors: Dong, Yuxian, Liu, Yanxin
Institution: Dalian University of Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223233386