Problems in additive number theory, V: Affinely inequivalent MSTD sets

TL;DR

This paper proves the existence of infinitely many affinely inequivalent MSTD sets of various sizes, highlighting ongoing open problems in additive number theory.

Contribution

It establishes that for infinitely many sizes, there are infinitely many affinely inequivalent MSTD sets, advancing understanding of their structure and diversity.

Findings

Existence of infinitely many affinely inequivalent MSTD sets for infinitely many sizes

Identification of open problems related to MSTD sets

Contribution to the classification of MSTD sets in additive number theory

Abstract

An MSTD set is a finite set of integers with more sums than differences. It is proved that, for infinitely many positive integers $k$, there are infinitely many affinely inequivalent MSTD sets of cardinality $k$. There are several related open problems.