Hou-Shan Fu

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...