## A New Bijection between Natural Numbers and Rooted TreesPeter Cappello ## AbstractA bijection is defined recursively between the set of natural numbers and the set of finite rooted trees. It is based on the prime decomposition of a natural number and the rank of a prime. This bijection leads naturally to a canonical presentation of rooted trees. For trees in each of two classes, bounds are given for the number of nodesin terms of the number assigned to the tree. ## BibTex@techreport{cappello:1988:bijection,author = {Peter Cappello}, title = {{A New Bijection between Natural Numbers and Rooted Trees}}, institution = {Computer Science, UC Santa Barbara}, year = {1988}, type = {}, number = {}, month = {}, note = {Presented at the 4th SIAM Conference on Discrete Mathematics, San Francisco, June 1988}, } ## Full version (pdf) |