Correspondences between plane trees and binary sequences

Abstract

The subject of each of the five sections of this paper is the planted plane trees discussed by Harary, Prins, and Tutte [7]. A description of the content of the present work is given in Section 1. Section 2 is devoted to a definition of plane trees in terms of finite sets and relations defined on them—we hope this definition will replace the topological concepts introduced in [7]. A one-to-one correspondence between the classes of isomorphic planted plane trees with n+2 vertices and the classes of isomorphic 3-valent planted plane trees with 2n+2 vertices is given in Section 3. Sections 4 and 5 deal with enumeration problems.