Cut trees in the topological analysis of branching patterns (Q792896)

The authors consider a quantity \(p(m| n)\) which is the probability that a subtree within a tree of degree n (number of terminal segments) randomly selected from a set of nth degree trees is of degree m (\(m\leq n)\). They derive recursive formulas for \(p(m| n)\) under various assumptions on the distribution of trees of degree n. These formulas then enable to quantify the consequences of random cutting of trees.