Lower bounds on the rotation distance of binary trees

The rotation distance d(S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T. While it is known that d(S,T)⩽2n−6, a well-known conjecture states that there are trees for which this bound is sharp for any value of n⩾11. We are unable to prove the conjecture, but we give here some simple criteria for lower bound evaluation, leading for example to individuate some “regular” tree structures for which d(S,T)=3n/2−O(1), or d(S,T)=5n/3−O(1).