A formal identity involving commuting triples of permutations

TL;DR

This paper proves a formal power series identity connecting the sum-of-divisors function to commuting triples of permutations, confirming a conjecture by Adams-Watters.

Contribution

It introduces a novel formal identity linking number theory and permutation group theory, resolving a conjecture in the field.

Findings

Established a new formal power series identity.

Linked arithmetic functions to permutation group properties.

Confirmed a conjecture of Franklin T. Adams-Watters.

Abstract

We prove a formal power series identity, relating the arithmetic sum-of-divisors function to commuting triples of permutations. This establishes a conjecture of Franklin T. Adams-Watters.