An equivalence between a conjecture of Neumann-Praeger on Kronecker classes and a conjecture on cliques of derangement graphs

TL;DR

This paper establishes a surprising equivalence between a conjecture in algebraic number theory related to Kronecker classes and a conjecture in combinatorics concerning cliques in derangement graphs, linking two distinct mathematical areas.

Contribution

It proves an equivalence between two conjectures from different fields, providing new insights and potential pathways for resolving both conjectures.

Findings

Proves the equivalence between the two conjectures.

Links algebraic number theory with combinatorics.

Provides a new perspective for approaching both conjectures.

Abstract

We prove an equivalence between a conjecture of Neumann and Praeger on Kronecker classes in algebraic number fields, and a conjecture on cliques of derangement graphs in combinatorics.