Complex Circles of Partition and the Expansion Principles

TL;DR

This paper extends the theory of circles of partition into the complex plane, introducing complex circles and using the squeeze principle to analyze partition possibilities in this new setting.

Contribution

It generalizes classical partition frameworks to the complex plane, providing new tools and concepts for complex partitions.

Findings

Introduces the notion of complex circles of partition.

Extends the classical framework from natural numbers to the complex plane.

Uses the squeeze principle to analyze partition possibilities.

Abstract

In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to partitions defined within the complex plane, which now serves as both the base and bearing set. We employ the squeeze principle as a central tool for rigorously investigating the possibility to partition numbers with base set as a certain subset of the complex plane.