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).