11 problems

Let $G=(V,E)$ be a connected multigraph, and let $\operatorname{Rel}(G;q)$ be its all-terminal reliability polynomial. Define … Let $\overline{\mathbb{D}}$ denote the closed unit d…

Let $G$ be a loopless connected graph, let $R_G({\bf p})$ be its multivariate reliability polynomial, and let $C_G({\bf v})$ be the connected-spanning-subgraph polynomial related b…

Let $G$ be a connected graph, and let $R_G(p)$ be its univariate reliability polynomial, obtained by setting all edge-operation probabilities equal to $p$. Univariate Brown–Colbour…

Let $G$ be a tree with $n$ vertices, and let $S(G;x)$ denote its subtree polynomial. The Brown–Mol annulus conjecture. Every root $x$ of $S(G;x)$ lies in the annulus … Brown and Mo…

The real-part boundedness conjecture. The set $\{\operatorname{Re}w:w\in\mathcal S\}$ is bounded above but is not bounded below. This conjecture asserts an asymmetric distribution…

Let $S_n(\lambda)$ be the Stern polynomial sequence defined by $S_0(\lambda)=0$, $S_1(\lambda)=1$, and … Let $\mathcal S$ denote the set of all complex zeros of the Stern polynomia…

Ulas's conjecture. For every $\varepsilon>0$ and every $m\geq 2$, there exists $N$, possibly depending on $\varepsilon$ and $m$, such that

Brilleslyper and Schaubroeck's conjecture. The number of roots of $x^n+x^m-1$ in the interior of the unit circle is

Annulus conjecture. The subtree roots of $T$ are contained in this annulus.

Disk conjecture. The subtree roots of $T$ lie in $D_n$.

Let … be a Weyl polynomial, with $a_i=b_i/\sqrt{i!}$ and $b_0,\ldots,b_n$ i.i.d. standard Gaussian random variables. Let $\mu_P$ denote the empirical measure of the roots of $P$. G…