On the Altitude of Nodes in Random Trees

Abstract

Let T n denote a tree with n nodes that is rooted at node r. (For definitions not given here see [ 4 ] or [ 10 ].) The altitude of a node u in T n is the distance α = α (u, T n ) between r and u in T n . The width of T n at altitude is the number W k = W k (T n ) of nodes at altitude in T n , where = 0, 1, …