7 problems

Fortuna's conjecture. The solution $X$ is entrywise nonnegative.

Higher-order trek-polynomial conjecture. The polynomial is

Let $B=\operatorname{diag}(b_1,\ldots,b_k)$ with $b_i<1$ for all $i$, let $H=\operatorname{diag}(h_1,\ldots,h_n)$, and let $\Gamma\in\mathbb{R}^{n\times k}$ and…

Factorization conjecture. The determinant of $A(\Sigma)_{\cdot,E}$ factorizes as

A continuation method traces stationary probability density functions of stochastically forced systems by solving Lyapunov or generalized Lyapunov equations, with previous solution…

Let a Lyapunov operator be represented by the relevant Kronecker-sum expression, and consider its singular values and singular vectors. Byers–Nash smallest-singular-vector conjectu…

Lyapunov representation conjecture. There exists a symmetric matrix $P=P^{\top}$ satisfying