5 problems

Let $B_n$ be the type B polynomials defined in the paper, for $n\geq 1$. A polynomial is real-rooted if all of its roots are real. Type B real-rootedness conjecture. For all…

Let $A_n$ be the polynomials introduced in the paper for $n\geq 1$. A polynomial is real-rooted if all of its roots are real. Aluffi–Chen–Marcolli's conjecture. The polynomials…

For each positive integer $n$, let $N_n(x)$ be the type A minuscule polynomial … A real polynomial is weakly Hurwitz stable if it is non-vanishing or identically zero when…

For $n\in\mathbb{N}$, define … These are the minuscule polynomials of type A. Bourn–Erickson's real-rootedness conjecture. The polynomial $N_n(x)$ has only real zeros for each…

Kirillov–Melnikov conjecture. The same sequence of polynomials arises in a number of different ways.