The inverse Erdos-Heilbronn Problem for restricted set addition in finite groups

TL;DR

This paper surveys additive combinatorics problems related to the Cauchy-Davenport and Erdos-Heilbronn theorems, extending inverse results in cyclic groups and providing counterexamples in nonabelian groups.

Contribution

It extends an inverse theorem in cyclic groups and presents a counterexample to a conjecture in nonabelian groups, advancing understanding of inverse problems in additive combinatorics.

Findings

Extended inverse theorem of Dias da Silva-Hamidoune in Z/pZ

Counterexample to an open conjecture in nonabelian groups

Survey of direct and inverse problems in additive combinatorics

Abstract

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in Additive Combinatorics. We prove a slight extension to an inverse theorem of Dias da Silva-Hamidoune in Z/pZ, and we present a counterexample to an open conjecture concerning the inverse Erdos-Heilbronn problem in nonabelian groups.