3 problems

Nilpotence conjecture. For all $a\geqslant 0$, $b\geqslant 0$, and $k\geqslant 0$, there exists an integer $N\geqslant 0$ such that every entry of

Let $n$ be an even integer, possibly nonpositive, and let $j>0$. Set … Let $t$ be either the sequence $(-1)v^{j-1}$ or the sequence $v^{j-1}n$; both have length $2j-1$. The map…

Maximal-orbit conjecture for $C_{1,n}$. The orbit of $t$ under the map $C_{1,n}(1,-)$ has length $2^j$. The general orbit bound proved in the source shows that this is the maximum…