8 problems

Hawaiian conjecture. Each chord of $\mathcal{G}_{P}$ contains at least one nonreal zero of $P$.

Craven–Csordas–Smith conjecture. The polynomial $W(P,P')$ has at most $2s$ real zeros.

Mean-value formula conjecture. The mean value is equal to

Let $B_{5/27}(1)$ denote the disk of radius $5/27$ centered at $1$, and let $Z(G;q)$ be the chromatic polynomial of a series-parallel graph $G$. The punctured-disk zero-free conjec…

Let $P_{n,k}(t)$ be the generating polynomial associated with the Lah distribution. Negative-real-part zeroes conjecture. All complex zeroes of $P_{n,k}$ have negative real parts.…

For each integer $\Delta\geq 3$, let $\mathcal{G}_\Delta$ be the class of graphs of maximum degree at most $\Delta$, and let … where $Z_G(\lambda)$ is the independence polynomial o…

Generalized Hawaii conjecture. If $\varkappa>\dfrac{n-1}{n}$, then

Let $G$ be a finite planar self-dual lattice, or let $G$ be the square lattice with free or periodic boundary conditions in the thermodynamic limit. For $q\geq 1$, introduce $v$ by…