A note on growing binary trees

The class ⊤ of binary search trees is studied. A leaf is a vertex of degree 0; ⊤n is the subset of ⊤ consisting of trees with n leaves. We grow trees in ⊤n from ⊤n - 1 thereby inducing a probability measure on ⊤n. We will show that the expected value of the average leaf distance of t ∈ ⊤n is asymptotic to log2n as n → ∞. © 1973.