3 problems

Let $D_n$ be the dihedral group, with order-$n$ cyclic subgroup generated by the usual rotation. Let $S$ be a generating set composed of three involutions, none of which belongs to…

The minimum-length conjecture. For every odd $n\geq 3$, every $r\in[n-1]$, and every $T\in\mathrm{Tour}_n$,

The extremal length conjecture. For every $n\geq 3$, $r\in[n-1]$, and $T\in\mathrm{Tour}_n$,