6 problems

Strong inverse $Z$-polynomial log-concavity conjecture. For any matroid $\mathrm{M}$ equipped with an action of a finite group $W$, the coefficients of the equivariant inverse $Z$-…

Equivariant unimodality conjecture. For any matroid $\mathrm{M}$ equipped with an action of a finite group $W$, the coefficients of its equivariant inverse $Z$-polynomial are equiv…

For integers $m$ and $d$, and $0\leq i\leq d$, define … A finite sequence of real numbers is an $n$-sequence when the associated polynomial has real zeros of one common sign. The…

Proudfoot–Xu–Young's conjecture. The polynomial $Z_M(t)$ has only negative zeros for every matroid $M$. The source gives no resolution of this conjecture for arbitrary matroids.

Let $\{M_d\mid d\geq 0\}$ be a nice family of matroids, and let $Z_d(t)$ denote the $Z$-polynomial associated with $M_d$. For polynomials with real roots, say that $f(t)$ interlace…

Let $M$ be a matroid, and let $Z_M(t)$ denote its $Z$-polynomial. The real-rootedness conjecture. All roots of $Z_M(t)$ lie on the negative real axis. This is the $Z$-polynomial an…