9 problems

Degree-eight distinct-diagonal test case. Every reducible connected degree-eight spectral curve is obtained from a constant branch or from reversal symmetry. In particular, there i…

Amended reducibility conjecture. Every reducible factorization of $\chi_n$ is expected to be obtained by iterating the following operations on connected blocks: cutting the chain a…

Strong nonvanishing conjecture. The operator $M^*(s,\rho_c(\tau_a)\otimes \rho_d(\tau_b))$ is nonzero for every $s\in\mathbb{C}$.

Let $G$ be a reductive group, let $P=MN$ be a parabolic subgroup, and let $I^G_P(\sigma)$ be the parabolic induction of an irreducible admissible representation $\sigma$ of $M$. Su…

McDiarmid–Reed reducibility conjecture. For every hexagonal graph $G$, $\operatorname{core}_{\mathcal{F}_{9,4}\cup\mathcal{F}'_{9,4}}(G)$ is $(9,4)$-colorable.

Squarefreeness conjecture. The polynomial $F_{m,n}$ has no multiple roots.

Monotonicity conjecture. If $C_r(\mathcal{N}_n)$ is reducible, then $C_r(\mathcal{N}_{n+1})$ is reducible.

A trellis represents a code, and a trellis is nonminimal when it is not minimal for that code. A reduction procedure consists of the reduction steps from the proof of Theorem; stat…

Three-linear-factor conjecture. There are no trinomials $x^n+A x+B$ defined over $\mathbb{Q}$ with reducibility type $(1,1,1,n-3)$.