4 problems

Let $K$ be a field of characteristic zero, let $R=K[t_i\mid i\ge 0]$, and let $L=\operatorname{Lie}(v_1,v_2)\subset\operatorname{Der}R$. Characteristic-zero growth problem. Determi…

Let $W_N$ be the set of standard monomials of length $N$ in the Fibonacci Lie algebra, and regard their multidegrees as points in the plane. Two-line-family conjecture. For every f…

Let $\mathcal L$ be the Fibonacci Lie algebra, let $\gamma_{\mathcal L}(n)$ denote its regular growth function, and let $\lambda=(1+\sqrt 5)/2$. Growth-limit conjecture. The normal…

Growth-constant bound conjecture. There exists a function $F:(0,\infty)\rightarrow(0,\infty)$ such that $A$ has at most $F({\rm GC}(A))$ prime ideals $P$ satisfying…