The Structure of Z-related sets

TL;DR

This paper explores Z-related sets in cyclic groups, providing a complete enumeration for small cases and revealing a permutation group action that models their relations.

Contribution

It introduces a comprehensive enumeration of Z-related sets in small cyclic groups and demonstrates a permutation group action representing their Z-relations.

Findings

Complete enumeration of Z-related sets for small N in cyclic groups.

Identification of a permutation group action modeling Z-relations.

New computational results on the structure of Z-related sets.

Abstract

The paper presents some new results on Z-related sets obtained by computational methods. We give a complete enumeration of all Z-related sets in $\mathbb{Z}_{N}$ for small $N$. Furthermore, we establish that there is a reasonable permutation group action representing the Z-relation.