The Rosenberg-Strong Pairing Function

TL;DR

This paper surveys the properties and applications of the Rosenberg-Strong pairing function, comparing it to Cantor's pairing function, and discusses its advantages in practical enumeration problems like binary trees.

Contribution

It provides a comprehensive overview of the Rosenberg-Strong pairing function, including its generalizations and practical benefits over Cantor's pairing function.

Findings

Rosenberg-Strong pairing function has advantages in practical applications.

It can be generalized to higher dimensions.

Application to enumerating full binary trees.

Abstract

This article surveys the known results (and not very well-known results) associated with Cantor's pairing function and the Rosenberg-Strong pairing function, including their inverses, their generalizations to higher dimensions, and a discussion of a few of the advantages of the Rosenberg-Strong pairing function over Cantor's pairing function in practical applications. In particular, an application to the problem of enumerating full binary trees is discussed.