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Hou-Shan Fu

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Preprint Oct 2026

A rank bound for bases and circuits in binary matroids

Let $b(M)$, $d(M)$, and $r(M)$ denote the number of bases, the number of circuits, and the rank of a matroid $M$, respectively. We prove that every nonempty simple binary matroid with no coloops satisfies \[ 2b(M)\ge(r(M)+1)d(M), \] with equality if and only if $M$ is isomorphic to the Fano matroid. This conf...

Hou-Shan Fu · 0 citations

Preprint Sep 2026

Real-rootedness and ultra log-concavity of rank-two matroid Ehrhart $h^*$-polynomials

We prove that the Ehrhart $h^*$-polynomial of a rank-two matroid with exactly three parallel classes is real-rooted whenever its smallest parallel class has size at most three. This bound is sharp: the rank-two matroids with parallel-class sizes $(4,561,600)$ and $(4,a,a+29)$, for all sufficiently large integers $a$, h...

Hou-Shan Fu · 0 citations