Inverse problems in Additive Number Theory and in Non-Abelian Group Theory

TL;DR

This paper explores new inverse and direct results in additive number theory related to Minkowski sums and connects these findings to inverse problems in non-abelian Baumslag-Solitar groups, advancing understanding in both areas.

Contribution

It introduces novel results in additive number theory and establishes a link to inverse problems in Baumslag-Solitar groups, bridging abelian and non-abelian group theories.

Findings

New results on Minkowski sums of dilates

Connections between additive number theory and non-abelian group problems

Solutions to inverse problems in Baumslag-Solitar groups under small doubling conditions

Abstract

The aim of this paper is threefold: a) Finding new direct and inverse results in the additive number theory concerning Minkowski sums of dilates. b) Finding a connection between the above results and some direct and inverse problems in the theory of Baumslag-Solitar (non-abelian) groups. c) Solving certain inverse problems in Baumslag-Solitar groups or monoids, assuming appropriate small doubling properties.