4 problems

Kececioglu–Sankoff conjecture. Every linear permutation has an optimal sorting by reversals in which no reversal cuts a strip except possibly at its first or last element.

Let $[n]^{\pm}$ be the signed set, and let … and … be long cycles on $[n]^{\pm}$. Set $\pi=p\circ s$. Chen–Reidys cycle conjecture. The elements $n$ and $s_n$ belong to the same cy…

Cycle-membership conjecture. The elements $n$ and $s_n$ belong to the same cycle of $\pi$.

Cycle-membership conjecture. The elements $n$ and $s_n$ belong to the same cycle of $\pi$.