8 problems

Defant's conjecture.

Let $R_n$ denote the reverse permutation on $n$ symbols. A prefix transposition moves a prefix of a permutation to a later position while preserving the order of the moved symbols…

Let $S_n$ be the set of permutations of $n$ symbols, and let the prefix transposition distance of a permutation be the minimum number of prefix transpositions needed to sort it. Th…

Let a permutation with $n$ symbols be given. A prefix transposition moves a prefix of the permutation to a later position while preserving the order of the moved symbols and the re…

Hannenhalli–Pevzner extension conjecture. The result of Hannenhalli and Pevzner for linear partially signed permutations extends to partially signed circular permutations in the sa…

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.

Upper-bound conjecture. There always exists a cyclically adjacent swap such that

Wastlund's conjecture. If $n\neq 13$ and $n\neq 15$, then every $n$-permutation can be sorted by at most