10 problems

Let $M$ be a matroid, and let ${\mathcal S}$ be an $r$-uniform set system with generating polynomial … The basis generating polynomial of $M$ is…

The Fano matroid $F_7$, the non-Fano matroid $F_7^-$, their relaxations $F_7^{--}$, $F_7^{-3}$ and $M(K_4)+e$, the matroids $P_8$, $P'_8$ and $P”_8$, the Pappus and non-Pappus matr…

Rank-three transversal matroid conjecture. Every rank-$3$ transversal matroid has the half-plane property.

Strongly base-orderable matroid conjecture. Every strongly base-orderable matroid has the half-plane property.

Minor-minimal obstruction conjecture. The non-half-plane-property matroids listed in the source beyond the first six are also minor-minimal, and the set of minor-minimal non-half-p…

Rank-three transversal matroid conjecture. Every transversal matroid of rank $3$ has the half-plane property.

A quaternionic unimodular matroid is a matroid representable by a quaternionic unimodular matrix. A matroid has the half-plane property when its bases-generating polynomial is stab…

A matroid has the weak half-plane property when its set of bases agrees with the support of a stable polynomial. A relaxation of a matroid is obtained by relaxing a circuit-hyperpl…

Huh's conjecture. The correlation constant cannot exceed

Let $\mathcal{M}$ be a matroid with the weak half-plane property, and let a relaxation of $\mathcal{M}$ mean a matroid obtained by relaxing a circuit-hyperplane of $\mathcal{M}$. R…