8 problems

Stabilized-difference conjecture. Recall the integers $c_{n,2}^\bullet(k)$ introduced in Appendix B. We conjecture that, for each fixed $k\ge0$,

Diagonal-gcd conjecture. For all $n$,

Denominator-relation conjecture. For all $n$,

Vanishing-numerator conjecture. For $n\ge5$,

Binomial-denominator conjecture. The denominators $D(C_{n,2};s,t)$ and $D(T_{n,2};s,t)$ can be written as products of binomials $1-s^a t^b$, where $a$ and $b$ are nonnegative integ…

Let $M_n(F)^ell$ be the variety of $ell$-tuples of $n\times n$ matrices, and let $\mathcal G_n(\ell)$ be the group of automorphisms induced by automorphisms of the free algebra wit…

Let $n$ and $d$ denote the parameters of the trace algebra considered in the source, and let $N^1(n,d)$ denote the quantity measuring the relevant first relation degree. Bound conj…

Let $R$ be an evaluation map obtained from the trace reduction referred to in the source, and let the chosen monomials be the monomials used to construct the corresponding generati…