A weighted inequality for matroid flats and log-concavity of Whitney numbers

Yuxian Dong; Yanxin Liu

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arXiv · 2610.29893

A weighted inequality for matroid flats and log-concavity of Whitney numbers

Yuxian Dong·Yanxin Liu

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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.

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Yuxian Dong, Yanxin Liu. 2026-10-21. A weighted inequality for matroid flats and log-concavity of Whitney numbers. https://arxiv.org/abs/2610.29893

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