A One-to-One Correspondence between Natural Numbers and Binary Trees
This work provides a theoretical mapping between number theory and tree structures, which is incremental in mathematical combinatorics.
The paper establishes a one-to-one correspondence between natural numbers (excluding 1) and a specific set of binary trees, where each number is characterized by a type and order pair.
A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.