Author

Yu-Xian Dong

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Preprint Oct 2026

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

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 equalit...

Yu-Xian Dong, Yan-Xin Liu · 0 citations

Preprint Sep 2026

Combinatorial aspects of the Delannoy Lattice

The Delannoy numbers $d(n,k)$ count lattice paths from $(0,0)$ to $(n-k,k)$ using steps $(1,0),(0,1)$ and $(1,1)$. This paper introduces a graded poset $\mathcal{D}_n$ on the Delannoy paths ending on the line $x+y=n$, whose rank-generating function is the Delannoy polynomial $d_n(x)=\sum_{k=0}^n d(n,k)x^k$. We prove th...

Xi Chen, Yu-Xian Dong · 0 citations