Preprint.
Ömer Egecioglu and Peter Cappello
A Bijection with Applications to Asymptotic Properties of Rooted Trees
Abstract.
We construct a bijection between rooted trees and natural numbers based on the
prime decomposition of a natural number and the rank of a prime. The bijection
leads naturally to a canonical presentation of rooted trees. Based on a conjecture
in additive number-theory, the bijection also provides for asymptotic distribution of
rooted trees by the number and the structure of principal subtrees.
omer@cs.ucsb.edu