Proximity Inversion Functions on the Non-Negative Integers

TL;DR

This paper introduces a novel method for constructing functions on non-negative integers that satisfy specific proximity conditions, conjectures optimality of the supremum, and presents open problems for further research.

Contribution

The paper proposes a new construction method for proximity inversion functions and conjectures their supremum is optimal, advancing understanding in this mathematical area.

Findings

Constructed a new class of proximity inversion functions.

Conjectured the optimality of the supremum of these functions.

Posed open problems for future investigation.

Abstract

We consider functions mapping non-negative integers to non-negative real numbers such that a and a+n are mapped to values at least 1/n apart. In this paper we use a novel method to construct such a function. We conjecture that the supremum of the generated function is optimal and pose some unsolved problems.