4 problems

Let $\mathsf{M}$ be a matroid, and write its inverse $Z$-polynomial as $Y_{\mathsf{M}}(t)=a_0+a_1t+\cdots+a_nt^n$. A coefficient sequence is unimodal if it increases and then decre…

Let $\mathsf{M}$ be a matroid, and let $Z_{\mathsf{M}}(t)$ denote its $Z$-polynomial. Proudfoot–Xu–Young conjecture. For any matroid $\mathsf{M}$, all roots of $Z_{\mathsf{M}}(t)$…

Let $\mathsf{M}$ be a matroid, and let $g_{\mathsf{M}}(t)$ denote its $g$-polynomial. g-polynomial positivity conjecture. The polynomial $g_{\mathsf{M}}(t)$ has positive coefficien…

Let $\mathsf{M}$ be a matroid of rank $k$, and write its Z-polynomial in the form … where $\gamma_{\mathsf{M}}(t)$ is the associated gamma-polynomial. Gamma-positivity conjecture.…