Classification of unstable circulants of square-free order

TL;DR

This paper proves Wilson's conjecture for unstable circulants of square-free order, showing that all such nontrivially unstable circulants have Wilson type, and identifies minimal criteria needed for this classification.

Contribution

The paper confirms Wilson's conjecture for a specific class of circulants and simplifies the criteria required for their classification.

Findings

Wilson's conjecture holds for square-free order circulants.

Only criteria (C.1) and (C.4) are necessary for classification.

All nontrivially unstable circulants of this type have Wilson type.

Abstract

In this paper we prove that for circulants of squarefree orders Wilson's conjecture hold, that is each nontrivially unstable circulant of such order has Wilson type. We show that actually only criteria (C.1) and (C.4) are needed.