On the rotation distance between binary trees

Abstract: We develop combinatorial methods for establishing lower bounds on the rotation distance between binary trees, i.e., equivalently, on the flip distance between triangulations of a polygon. These methods lead to sharp estimates for certain particular pairs of trees. As an application, we prove that, for each n, there exist size n trees at distance , i.e., the diameter of the nth associahedron has at least this value. [Copyright &y& Elsevier]