Computerizing the Andrews-Fraenkel-Sellers Proofs on the Number of m-ary partitions mod m (and doing MUCH more!)

TL;DR

This paper simplifies and generalizes proofs regarding the mod m characterization of m-ary partitions, extending their scope and depth using computational methods to handle more cases and prove deeper theorems.

Contribution

It introduces a streamlined approach to existing proofs and extends their applicability to broader cases with the aid of computer-assisted methods.

Findings

Simplified proofs of mod m characterization of m-ary partitions

Generalized theorems to cover more cases

Used computational tools to prove deeper results

Abstract

In this short article, two recent beautiful proofs of George Andrews, Aviezri Fraenkel, and James Sellers, about the mod m characterization of the number of m-ary partitions are simplified and streamlined, and then generalized to handle many more cases, and prove much deeper theorems, with the help of computers, of course.