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).