Bounding restricted rotation distance

Restricted rotation distance between pairs of rooted binary trees quantifies differences in tree shape. Cleary exhibited a linear upper bound of 12n for the restricted rotation distance between two trees with n interior nodes, and a lower bound of (n − 1)/3 if the two trees satisfy a reduction condition. We obtain a significantly improved sharp upper bound of 4n− 8 for restricted rotation distance between two rooted binary trees with n interior nodes, and a significantly improved sharp lower bound of n − 2, again with the requirement that the trees satisfy a reduction condition. These improvements use work of Fordham to compute the word metric in Thompson’s group F .