Problems in additive number theory, VI: Sizes of sumsets

TL;DR

This paper explores the possible sizes of sumsets and restricted sumsets within finite subsets of integers and ordered abelian groups, addressing fundamental problems in additive number theory.

Contribution

It investigates the range of cardinalities of sumsets and restricted sumsets, providing new insights into their possible sizes in various algebraic structures.

Findings

Characterization of sumset sizes in finite integer subsets

Analysis of restricted sumset cardinalities in ordered abelian groups

Identification of open problems in additive number theory

Abstract

This paper describes problems concerning the range of cardinalities of sumsets and restricted sumsets of finite subsets of the integers and finite subsets of ordered abelian groups.