Counting MSTD Sets in Finite Abelian Groups

TL;DR

This paper derives asymptotic formulas for counting MSTD sets in finite abelian groups, extending prior work and utilizing advanced combinatorial graph theory results.

Contribution

It provides the first asymptotic enumeration of MSTD sets in finite abelian groups, connecting additive combinatorics with graph theory.

Findings

Asymptotic formulas for MSTD sets in finite abelian groups

Extension of Nathanson's previous results

Application of Alon and Kahn's conjecture on independent sets

Abstract

In an abelian group G, a more sums than differences (MSTD) set is a subset A of G such that |A+A|>|A-A|. We provide asymptotics for the number of MSTD sets in finite abelian groups, extending previous results of Nathanson. The proof contains an application of a recently resolved conjecture of Alon and Kahn on the number of independent sets in a regular graph.