On Symmetric Invertible Binary Pairing Functions

TL;DR

This paper introduces a symmetric invertible binary pairing function for positive integers, proves its properties, and discusses how to construct similar functions on other integer sets, advancing mathematical tools for pairing functions.

Contribution

The paper presents a new symmetric invertible binary pairing function and provides a complete proof of its symmetry and bijectivity, enabling construction on various integer sets.

Findings

Constructed a symmetric invertible binary pairing function.

Provided a complete proof of symmetry and bijectivity.

Outlined methods for constructing such functions on different integer sets.

Abstract

We construct a symmetric invertible binary pairing function $F(m,n)$ on the set of positive integers with a property of $F(m,n)=F(n,m)$. Then we provide a complete proof of its symmetry and bijectivity, from which the construction of symmetric invertible binary pairing functions on any custom set of integers could be seen.