3 problems

Let $\mathcal{Q}$ and $R_{m,n}$ be as above. For $F\in R_{m,n}$, let $Z$ denote the innermost polynomial of $F$. The vanishing innermost-polynomial conjecture. If…

Let $\mathcal{Q}$ and $R_{m,n}$ be as above. For a polynomial $F\in R_{m,n}$, let $W_F$ be the $F$-generator constructed in the paper, and let $\mathbb{T}$ be the corresponding cla…

Let $q$ be a prime power, and let $k,l$ be positive integers. Write $c\mathcal{F}_k(q)$ for the set of elements of degree $k$ over $c\mathbb{F}_q$. Existence conjecture. There exis…