The conjugation diameter of a group is the largest diameter of its Cayley graphs with respect to conjugation-invariant generating sets. It is a strong form of the extensively studied concept of the diameter of . We compute the conjugation diameter of the symmetric groups.
"Conjugation diameter of the symmetric groups." Involve 13 (4) 655 - 672, 2020. https://doi.org/10.2140/involve.2020.13.655